Cutting a starkly different image from Mr. Trump’s more combative and impulsive public supporters, like Chris Christie or Sarah Palin, not to mention the candidate himself, Ms. Trump, 34, radiates disciplined poise and practiced reserve. While her father uses Twitter as a grenade launcher, she treats her well-tended social media feeds, which are notably politics-free, as marketing tools for the Trump Organization and her own line of women’s clothing and accessories.

On March 15, with her father in the midst of a political clear-cutting through Florida while facing accusations of stirring up racially charged violence at his rallies, she posted a photograph on Instagram highlighting the @TrumpHotels creative team in Waikiki under a serene image of a woman relaxing in a sun-dappled pool.

It was a fitting image for a devoted daughter who exists as an almost surreally detached counterpoint to her father’s bellicosity, and yet may be his most important ally, particularly if he finds himself facing a Democratic opponent who aspires to be the first female president of the United States.

Ms. Trump tried to do damage control after her father seemed to have made reference to Megyn Kelly’s menstrual cycle. She was the unlikely star of a CNN town hall program last week with the Trump family, talking about how her father had encouraged and empowered her. And in a recent interview at Trump Tower, Ms. Trump attacked, however gently, her father’s critics.

“What bothers me is how rash people are to make claims as if they knew him and they knew his viewpoint on certain topics,” she said. “My father has an enormous heart and truly loves people — all people.”

Inside her father’s campaign, which has brazenly eschewed the advice of political experts, Ms. Trump is one of a few people who can, on occasion anyway, influence the candidate’s thinking. She failed to persuade Mr. Trump to apologize for accusing Mexico of sending its “rapists” over the border, according to a person close to Mr. Trump who declined to be named because he was not authorized to speak for the campaign. But, this person said, she successfully convinced her father to maintain his qualified support for Planned Parenthood in the face of Republican criticism.