But they are warier of Ms. Trump, who only recently arrived in the West Wing and until now has been a more sporadic player than her ambitious husband. Initially resistant to a formal role in the administration, Ms. Trump took an office and a government position — albeit, like her husband, without accepting a salary — out of concern over the troubles of her father’s first couple of months in office.

According to associates, she views her role partly as guardian of the family reputation and has fretted during and since the campaign about the long-term damage to the family business’s image that her father’s political career could cause.

When Ms. Trump does intervene, her father listens — although he does not always take her advice. One person close to the family described her influence as a delayed-action fuse: At times the president will mention a point Ms. Trump made, uncredited, days later.

Her brother Eric Trump said she was upset by pictures of victims from the chemical attack in Syria and that may have encouraged their father to retaliate. He defended family members being in the White House, saying relatives are more candid. “The beautiful thing about family is you play on a little bit of a different dynamic and once in a while you can pull them aside and say, ‘No disrespect but you might want to think about this or maybe you crossed the line here,’” he told The Daily Telegraph.

The White House had no comment on Friday. But the supposed backstage liberal counterrevolution that critics fear has yielded modest results. Last week, the president signed legislation allowing states to deny federal funding to women’s health care providers offering abortion services, like Planned Parenthood. Ms. Trump and Mr. Kushner were skiing in Canada, just as they were on the slopes in Aspen during the collapse of the health care effort.

“I think there are multiple ways to have your voice heard,” Ms. Trump recently told CBS News. “In some cases, it’s through protest and it’s through going on the nightly news and talking about or denouncing every issue on which you disagree with. Other times it is quietly and directly and candidly.

“So where I disagree with my father, he knows it,” she added. “And I express myself with total candor. Where I agree, I fully lean in and support the agenda and — and hope — that I can be an asset to him and — and make a positive impact. But I respect the fact that he always listens. It’s how he was in business. It’s how he is as president.”