WASHINGTON — President Trump urged senators this month to repeal the Affordable Care Act’s requirement that most Americans have health insurance and use the proceeds to slash the top tax rate paid by the richest Americans, a suggestion that pitted his priorities against his daughter and Republican senators intent on helping the middle class.

In the end, the president accepted only a partial victory. He got the repeal of the health law’s individual mandate, but gave up on an income tax rate cut that would have directly benefited him personally. Instead, Ivanka Trump and her allies in the Senate prevailed in their push to include an expanded child tax credit.

“This was certainly an uphill battle, especially given that it is not an issue that is as widely understood,” said Senator Mike Lee, Republican of Utah and a leading advocate of the expanded child tax credit. “We didn’t necessarily have the sense that the president was opposed to it. I still don’t have that sense. I think if he had been, things would have worked out differently than they did.”

Two White House officials pushed back against the notion that Ms. Trump had split with her father. They said middle-income tax relief was one of the president’s priorities and that Ms. Trump worked in lock step with the administration on all aspects of tax reform.