A month before Donald J. Trump was elected president, he and his aides watched his daughter’s coolly composed surface crack open.

Inside Trump Tower, the candidate was preparing for a debate when an aide rushed in with news that The Washington Post was about to publish an article saying that Mr. Trump had bragged about grabbing women’s private parts. As Ivanka Trump joined the others waiting to see a video of the episode, her father insisted that the description of his comments did not sound like him.

When the recording finally showed he was wrong, Mr. Trump’s reaction was grudging: He agreed to say he was sorry if anyone was offended. Advisers warned that would not be enough.

Ivanka Trump made an emphatic case for a full-throated apology, according to several people who were present for the crisis discussion that unfolded in Mr. Trump’s 26th-floor office. Raised amid a swirl of tabloid headlines, she had spent her adult life branding herself as her father’s poised, family-focused daughter. She marketed her clothing line with slogans about female empowerment and was finishing a book on the topic. As she spoke, Mr. Trump remained unyielding. His daughter’s eyes welled with tears, her face reddened, and she hurried out in frustration.

Seven months later, Ms. Trump is her father’s all-around West Wing confidante, an adviser whose portfolio appears to have few parameters, making her among the highest-ranking women in a senior staff stocked almost entirely with men.

The two trade thoughts from morning until late at night, according to aides. Even though she has no government or policy experience, she plans to review some executive orders before they are signed, according to White House officials. She calls cabinet officials on issues she is interested in, recently asking the United Nations ambassador, Nikki R. Haley, about getting humanitarian aid into Syria. She set up a weekly meeting with Steven Mnuchin, the Treasury secretary.

In interviews last week, she said she intended to act as a moderating force in an administration swept into office by nationalist sentiment. Other officials added that she had weighed in on topics including climate, deportation, education and refugee policy.

Even as Ms. Trump said she was seeking to exert more influence, she acknowledged she was a novice about Washington. “I’m still at the early stages of learning how everything works,” she said, “but I know enough now to be a much more proactive voice inside the White House.”

Ms. Trump, 35, a former model, entrepreneur and hotel developer, says she will focus on gender inequality in the United States and abroad, by aiming to create a federal paid leave program, more affordable child care and a global fund for women who are entrepreneurs, among other efforts. Her interest in gender issues grew out of a “Women Who Work” hashtag and marketing campaign she devised a few years ago to help sell $99 pumps and $150 dresses. On Tuesday, the career advice book she worked on before the election, whose title echoes her hashtag, will be published.

By inserting herself into a scalding set of gender dynamics, she is becoming a proxy for dashed dreams of a female presidency and the debate about President Trump’s record of conduct toward women and his views on them. Critics see her efforts as a brash feat of Trump promotion — an unsatisfying answer to the 2005 “Access Hollywood” recording that surfaced during the campaign and the seas of pink, cat-eared “pussy hats” worn by protesters after the inauguration — by a woman of extraordinary privilege who has learned that feminism makes for potent branding. (Ms. Trump is not promoting her book for ethics reasons.)

In the two interviews last week, Ms. Trump talked about unleashing the economic potential of women — some of her phrases sounding uncannily like those of Hillary Clinton — and effused about finding a new role model in Eleanor Roosevelt, whose autobiography she is reading. Ms. Trump is reaching out to influential women like Ginni Rometty, chief executive of IBM, and Mary T. Barra, the C.E.O. of General Motors, and studying up on child care policy. She waved away questions about her motivations for embracing feminist themes.

“Suddenly, after my father declared his candidacy, it became that all the things that I was doing that I was praised for, the same people, the critics, viewed them through this different lens,” she said. “Somehow, all the same things they applauded me for as a millennial, as a female entrepreneur, were now viewed very cynically as opportunistic.”

Some former employees express surprise at her new policy interest, saying she was once reluctant to grant them maternity leave. But other observers call her the administration’s best hope for progress on gender issues and say they are encouraged to see a presidential daughter, and a top member of a Republican White House, advocate federal paid family leave. (She intends to go beyond her father’s campaign pledge and push to include both fathers and mothers, according to a White House official.)

“I hope she will go on to become a great champion in this area,” said Jim Yong Kim, president of the World Bank, which is working with Ms. Trump on funding female entrepreneurs.

Ultimately, “the only test is whether she is able to achieve something other than personal gain,” said Umber Ahmad, a banker turned baker and one of several women quoted in Ms. Trump’s new book who now say they feel uneasy about being included in it.

Those close to Ms. Trump say she is generally business-friendly and socially liberal. But she says that on many issues, she does not have strongly held views. (In the White House, she uses corporate terms — like “business plan” — as much as partisan or political ones.)

She has one skill unmatched by almost anyone else, family members and aides say: She can effectively convey criticism to a man who often refuses it from others, and can appeal to him to change his mind.

“I’m his daughter. I’ve known him my entire life. He trusts me,” she said. “I don’t have a hidden agenda. I’m not looking to hit him to help myself.”

Though their demeanors are different — she is guarded where he is unfettered — Ms. Trump is more like her father than most people realize, according to people who know them both.

She has his eye for image and branding, his sensitivity to perceived criticism. They are both skilled at the art of the sale. Like him, she sometimes makes sweeping, and arguably overreaching, claims: She portrayed Mr. Trump as an advocate for women in last summer’s convention speech, and described her brand as a stereotype-shattering movement. Like him, she appears confident she can master realms in which she has little expertise or experience. The two even speak in similar streams of superlatives: “tremendous,” “unbelievable.”

But can she influence his actions as president? In her 35 years, she has left little traceable record of challenging or changing the man who raised her. Mr. Trump did tape an apology for the “Access Hollywood” recording, but by then doing so had become a political necessity.

Mr. Trump summons Ms. Trump to the Oval Office to ask her questions and hear her ideas. (She calls him “Dad,” not “Mr. President.”) If he asks his daughter about an unfamiliar subject more than twice, she will often do research so she can develop a view. Sometimes she seeks out Mr. Trump, telling other staff members, “I need 10 minutes alone with my father.”

“A lot of their real interactions happen when it’s just the two of them,” Jared Kushner, Ms. Trump’s husband and fellow aide, said in a telephone interview.

Alone with her father, Ms. Trump makes the case on what she sees as priorities, she said. “I’ll go to the mat on certain issues and I may still lose those,” she said. “But maybe along the way I’ve modified a position just slightly. And that’s just great.”

The Loyal Daughter

No matter how high-decibel Mr. Trump’s divorces, no matter how outsize his statements, his daughter Ivanka rarely if ever rejected him, rebelled or distanced herself from him. When her parents’ marriage ended before she turned 10, photographers snapped her picture on the way to school and helicopters circled over Mar-a-Lago, Mr. Trump’s resort in Palm Beach, Fla. His public and private statements raised eyebrows.

“There were definitely times when I was younger I was going, ‘Did you have to say that, Dad?’ ” she told Oprah Winfrey in an interview.

Mr. Trump was always working. “He was not the father to go and play games with them in Central Park or take them for a walk,” Ivana Trump, Ivanka’s mother, told Michael D’Antonio, a biographer who shared his interviews with The Times. But Ivanka would stop by his office to say hello, or accompany him to construction sites, much as she sees him now in the West Wing or joins him on presidential excursions. She was impressed by her father’s empire; he praised her constantly to others.

Her older brother, Don Jr., was at boarding school when their parents divorced, and refused to speak to his father for a year; her younger brother, Eric, was very small. So Ivanka was the child who spent the most time with Mr. Trump, her mother said in an email to The Times. Even then, “Donald knew he could trust her!” she added.

As a teenager, Ms. Trump decided to try modeling, to make money and to show what she could accomplish on her own. She walked European runways, appeared on magazine covers, and was a co-host of her father’s Miss Teen USA Pageant. “She never stood a chance to have a normal modeling career because her name was associated with her dad,” said Audrey Roatta, who worked for the agency that represented Ms. Trump and accompanied her on trips.

Others were sometimes cutting about it: “She’s only here because of her dad,” Jennifer Lopez remarked within earshot of the teenage Ivanka at a movie premiere, Ms. Roatta recalled. (Representatives for both women said that they did not recall the incident.)

When her father started his own modeling agency a few years later, she was upset because he was sweeping into her domain — but she suppressed her anger, a friend said.

Just as Ms. Trump joined the family real estate business in 2005, the Trump name became even more of a source of power and opportunity because of the new glow from the reality television show “The Apprentice,” in which her father starred. Even as Ms. Trump was in her mid-20s, learning her way around financing negotiations and construction details, she played an authority figure on the show, weighing in on contestants’ merits during the tense boardroom scenes.

The attention helped her license her name to products: fine jewelry (2007), shoes (2010), clothing (2010) and handbags (2011), all of which were promoted on the show. Her business was closely intertwined with her father’s name and organization, where she continued to spend much of her time, initially relying on Trump Organization resources: payroll services, information technology and lawyers. (A representative for Ms. Trump said that she had reimbursed her father’s company.)

But penetrating the mass market presented a challenge: Ms. Trump’s gilded life felt distant to women who shopped at Macy’s. So, late in 2013, she and her husband gathered with a few employees in front of a whiteboard in their Upper East Side apartment. Sheryl Sandberg’s “Lean In” had just topped the best-seller charts, and Ms. Trump’s team wanted its own catchy yet accessible slogan.

The brainstorming solidified into a new motto: “Women Who Work.”

Cultivating an Image

Ms. Trump and her team set about tailoring her image to fit the concept. An internal document lists one of her challenges as “perceived as rich and unrelatable.” (An additional one: Most of her followers on social media were men.) Ms. Trump was told to post more down-to-earth pictures on her Instagram feed — less made-up model, more mommy.

She hesitated to showcase her young children, but “we certainly had conversations about whether it was O.K. to put her kids on social media and we felt it was important to show who she was as a whole person,” said Abigail Klem, president of the Ivanka Trump brand.

Her company pitched a never-made podcast that would feature Ms. Trump as a chic business guru, interviewing success stories and business-feminism leaders like Ms. Sandberg and Sara Blakely, founder of Spanx. The pitch described the supposed impact of the “Women Who Work” brand campaign: “the outdated caricature of a ‘working woman’ — frazzled, androgynous and entirely one-note — began to crack.”

But Ms. Trump’s brand had not always lived up to its progressive image. Initially, former employees say, Ms. Trump had been reluctant to grant maternity leave, and she did not have a benefits package when she began hiring people to work for her.

Marissa Kraxberger, a former executive who was pregnant when Ms. Trump offered her a job in the summer of 2013, recalled asking her future boss about paid leave. She described Ms. Trump as saying, “Well, we don’t have maternity leave policy here; I went back to work one week after having my child, so that’s just not something I’m used to.”

Ms. Kraxberger said that she and others pushed Ms. Trump to start offering a paid maternity leave policy. Ms. Klem said that the business was new when the issue arose, and that after consulting employees, the company put in place a policy for two-month paid family leave, as well as flexible working hours, in the summer of 2014.

Ms. Trump had not seemed especially focused on gender politics or policy, according to people who have known her at various points throughout her life, beyond awareness of being the rare woman in the male-dominated world of real estate.

“Definitely the brand changed her, and her interests really solidified,” said Ms. Klem, who took over the day-to-day operations of the Ivanka Trump brand after the election. Soon, her office had a play area where children could use crayons and toys while their parents worked.

An Unfamiliar Role

Later, Ms. Trump and those close to her described the period just before her father announced his candidacy as one of the most fulfilling of her life. She had managed to update her family’s brand from the older, flashy days, with sleek designs. She was personally developing a hotel at the site of the Old Post Office building in Washington, a historical property. And Vogue magazine profiled her as a paragon of millennial taste and accomplishment — a far cry from the tabloid coverage of her youth.

But the very first day of her father’s presidential campaign caused her problems: His remarks about Mexico’s sending rapists over the border caused two celebrity chefs to drop out of the Old Post Office project.

Ms. Trump was shocked by the heat and fury of the campaign. Before, she had gotten letters of admiration, calling her a role model; now many of the letters she received were scathing. “Everything that was ascribed to him suddenly, for my critics, became true of me,” she said.

Last week, speaking in her newly repainted West Wing office — stark white with metallic accents, a contrast to the creamy traditionalism of the rest of the West Wing — Ms. Trump appeared alternately energized, defensive and daunted. Behind the scenes, advisers say, she has been frustrated, unhappy about giving up her life in New York, and determined to prevail and make the best of a White House tour that she never expected. That morning, for the first time since she had moved into her Washington home, photographers had not gathered outside.

It was her first full week in the role of assistant to the president, and she had just hired a chief of staff and was setting up meetings. “There’s a lot I don’t know about how government works and how things get done, but I feel I know enough now that I can be much more proactive about the type of change and reform that I’d like to see happen,” she said.

Ms. Trump was leaving that evening for Germany, representing the administration on the world stage for the first time. She flew that night on a commercial jetliner, traveling with her Secret Service detail and Dina Powell, the former Goldman Sachs executive and current deputy national security adviser who has become Ms. Trump’s all-around guide in the administration. In Berlin, Ms. Trump appeared on a panel with some of the most accomplished women in the world: Angela Merkel, the German chancellor; Christine Lagarde, the managing director of the International Monetary Fund; and Chrystia Freeland, the Canadian foreign affairs minister. In contrast, Ms. Trump was introduced as the “first daughter.”

As she spoke, the audience murmured with skepticism (contrary to some news reports, Ms. Trump was not loudly booed). One moment, however, appeared more cutting. “The German audience is not that familiar with the concept of a first daughter,” the moderator asked. “I’d like to ask you, what is your role, and who are you representing: your father as president of the United States, the American people, or your business?”

“Well, certainly not the latter,” Ms. Trump said lightly, adding, “I am rather unfamiliar with this role.”

An Inescapable Shadow

Questions about her father trail Ms. Trump everywhere now. Javier Palomarez, the chief executive of the United States Hispanic Chamber of Commerce, has been in touch with her in recent months about immigration and entrepreneurship, but their conversations have also turned more personal.

In one of their earliest talks, soon after the inauguration, Ms. Trump hinted at her frustration. “Let’s talk about your dad,” she said to Mr. Palomarez. She asked if he would be “100 percent absolutely proud of everything that came out of your father’s mouth,” especially when his father was age 70. She acknowledged that there was a difference between their fathers, Mr. Palomarez said — hers is the president.

Playing the role of centrist advocate in a right-leaning administration would be a challenge for anyone, even those steeped in politics. As is the case with her father, Ms. Trump’s newness to Washington and preference for straight-ahead business negotiations can result in painful collisions.

During the campaign, Ms. Trump successfully pushed her father to praise Planned Parenthood from a Republican debate stage, a moment that created a stir at the time because of the party’s broad opposition to the organization’s abortion services. But more recently, with congressional Republicans threatening to cut all funding to Planned Parenthood (even though the women’s health organization says it receives no federal funding for abortions), Ms. Trump approached its president, Cecile Richards, with a proposal. Planned Parenthood should split in two, Ms. Trump suggested, with a smaller arm to provide abortions and a larger one devoted to women’s health services.

White House officials said Ms. Trump was trying to find a common-sense solution amid the roar of abortion politics. But Planned Parenthood officials said they thought Ms. Trump’s advice was naïve, failing to understand how central reproductive choice was to the group’s mission. Ms. Richards sharply criticized Ms. Trump for not publicly objecting to the Republican health care bill that failed in March, and Ms. Trump felt stung.

She complained in the interview that many advocacy groups were “so wedded to the headline of the issue that sometimes differing perspectives and new information, when brought to the table, are viewed as an inconvenience because it undermines the thesis.”

Despite the tension, Ms. Trump helped preserve and increase funding for women’s health in the government spending deal devised over the weekend, a White House official said. But the victory may be short-lived: The coming bill that would repeal the Affordable Care Act may include a measure to strike Planned Parenthood’s funding.

For now, Ms. Trump acknowledges how much she has to learn and asks the public to be patient with her.

“I do believe that in time I’ll get to the right place,” she said. “In the short run I’ll have missteps, and, in some cases, I’ll take shots that I could have avoided if I had publicly said what I think.”

“I’m really, really trying to learn,” she added.