Family team: US president Donald Trump and his daughter Ivanka talk via video conference with International Space Station Commander Peggy Whitson and Jack Fischer on the Space Station last Monday, from the Oval Office of the White House Photo: AP Photo/Susan Walsh

'Who do you represent, Ivanka? Your father, the American people or your business?"

As an opening gambit, the question put to the First Daughter at the start of last Tuesday's W20 Summit certainly echoed what people at home were thinking. There the 35-year-old businesswoman sat, flanked by the political heavyweights Angela Merkel and Christine Lagarde, betraying the merest hint of nerves as she embarked on the first foreign event in her new official capacity: adviser to the president.

The W20 summit, designed to promote women's economic empowerment, was a coming-out of sorts for Ivanka, and a high-pressure one at that. Imagine being seated alongside two of the most powerful women in the world, before a crowd steeled against any charm offensive? But when the audience began booing and hissing at Ivanka for describing her father as a "tremendous champion of supporting families", any tremulousness vanished.

"I know from my personal experience," she said - emboldened by the catcalls - "and the thousands of women who have worked with and for my father are testimony to his enormous belief in women's potential and the ability to do the job as well as any men. As a daughter, I know he encouraged me and enabled me to thrive. I grew up in a house where there were no barriers."

Minutes later she was drawing cheers. Ivanka had turned it around. "If you underestimate her," wrote one German commentator, "you've already lost."

Like many determined to write her off through lazy prejudice, I too underestimated Ivanka. As I rode up Trump Tower's gilded elevator to meet her for the first time back in 2012, part of me was expecting a Bergdorf Blonde playing at business in the corner office opposite daddy's.

The preconception overrode everything I'd been told about the smart Wharton Business School graduate, but women can sometimes have a stubborn mistrust of beautiful members of their sex. It took me minutes to realise how wrong I was about this startlingly bright and determined businesswoman. But at the end of Ivanka's first 100 days "in office", is the world ready to reassess its opinion of her, too?

"Ivanka appears poised to be an adviser, advocate and hostess all at once," says Kate Andersen Brower, author of First Women: The Grace and Power of America's Modern First Ladies. "Which could revolutionise the role and make her the most powerful First Lady ever."

Of course, there is already a First Lady - a certain Slovenian spitfire who has been married to the president for more than 20 years. But Melania Trump hasn't exactly hit the ground running. Still holed up in her $100m penthouse in New York with her 10-year-old son, Barron (at private school nearby), she has been elusive enough to be dubbed "Rapunzel, the beauty locked in a tower" by stylist Phillip Bloch, who has known the Trumps for two decades.

Certainly, the form of soft power traditionally epitomised by the First Lady - she usually has the president's ear over their morning granola and then last thing at night - seems to be absent in this scenario. And according to CNN political pundit Angela Rye, the "power vacuum" created by a missing Melania has left Trump with no choice but to parachute in his daughter as a kind of de facto First Lady. As senior adviser to the president, as she was officially named in March. The title does nothing to assuage Rye's concerns that "there's nothing to hold her accountable to in terms of benchmarks and she can tiptoe into conflicts of interest without any issue.

"We all know what role Ivanka is playing," she maintained, "and that's the role of First Lady because Melania is not checking for Donald."

In a detailed piece in this month's Vanity Fair, an anonymous member of the First Lady's fashion clan describes a growing mass hope that Melania "will leave him, and become this great feminist icon. She will walk into the middle of everything and say: 'He's crazy. This is nuts. I don't know what I was doing!'"

But I wouldn't hold out for a Rapunzel-themed tell-all - My Escape from Trump Tower? It seems more likely that this intensely private woman, who many say never wanted to be First Lady, will happily take a back seat while her stepdaughter fills "the power vacuum". Something she's already doing very efficiently.

She, her husband Jared Kushner, also a senior adviser to Trump, and their three children moved to a $5.5m house in Washington DC. For the first two months of her father's presidency, Ivanka lay low, giving CBS News a single interview. But she quietly began carving out an expanded role for herself well before she was given a formal title.

Trump's call in early March for affordable childcare, paid family leave and help for female entrepreneurs was widely seen as bearing Ivanka's signature, and it is said that both she and Kushner have intervened in the wording of executive orders on climate change and LGBT rights.

Last week the First Daughter dismissed her supposed influence on Syrian strikes as a "flawed interpretation", yet no one would deny that, in the past two months, Ivanka has emerged as a fixture in high-level meetings, sitting across from her father at a meeting with Homeland Security.

Yet, while she's successful in softening the edges of her father's agenda, it's her seat at the table - beside Merkel and Lagarde - that seemed to jar most.

While she is clearly "a bright woman", said Jeremy Mayer, a professor at George Mason University Schar School of Policy and Government, "nothing in her background suggests an aptitude for policy or politics at this level."

Couldn't the same be said of her father?

The fact remains that Ivanka's job is exactly what it was when I met the "executive vice president of development and acquisitions" at the Trump Organisation five years ago. She was her father's right-hand woman then, back when Trump's presidential ambition was a dinner party joke (made by him), and she's his right-hand woman now. Only the job description is more onerous - and subject to a lot of scrutiny.

This is also not the first time a daughter has fulfilled a First Lady-like role. Thomas Jefferson's daughter Martha Jefferson Randolph was said to have considerable influence over her father, as had Sarah-Yorke Jackson, daughter of Andrew Jackson, Mary Elizabeth Bliss (daughter of Zachary Taylor) and Mary Harrison McKee (daughter of Benjamin Harrison).

Ivanka was only eight when her father and mother split up, and despite tabloid reports that he had cheated on Ivana with model Marla Maples, Ivanka remained very close to him.

According to a family friend, when the coltish 15-year-old schoolgirl was at Choate Rosemary Hall boarding school in Connecticut, she would call her father every day - collect - from a pay phone in a janitor's closet. Meanwhile, colleagues remember Trump, ever the proud father, often bringing his daughter along to construction sites.

"My parents were the golden couple of New York," Ivanka told me back in that Trump Tower corner office in 2012.

"They were young, they were good-looking, they were charismatic and there was tremendous interest in covering them in the media. So I knew very early on that, no matter what I accomplished, there would always be someone saying: 'She would never have been able to do that without her parents.' And you know what? I can't argue with that, because it's a hypothetical."

Here I remember Ivanka pausing before resuming in a more strident tone: "Anyway, rather than dwell on it, I decided that what matters to me is that I'm respected by people I interact with, not people who have decided to dislike me.

"I do think that there is a binary outcome for the children of accomplished parents: either you're paralysed by the accomplishments of your parents and so afraid of failure that you don't put yourself out there at all, or you say: 'I am going to use this as motivation to work harder, try harder and learn more as I grow up.'"

All of which makes me wonder what Ivanka Trump will be doing in another 100 days' time.

I won't be under-estimating her this time.

Telegraph.co.uk