Mrs. Trump and the president have had a tumultuous relationship at times over the years, but few episodes have roiled the peace as much as the news surrounding Ms. Daniels. The reports of a payoff blindsided the first lady, who was furious with her husband, according to two people close to the couple. She has kept a low profile since…

This month, the East Wing has worked to swat down all manner of rumors about Mrs. Trump’s whereabouts and psyche, beginning with “Fire and Fury,” a book by Michael Wolff that described Mrs. Trump as a first-lady-to-be who had not supported Mr. Trump’s candidacy and cried on election night. Mrs. Trump, who is known to instruct her aides to publicly hit back at reports on her behalf, had them emphatically deny Mr. Wolff’s account.

After “Fire & Fury,” two people close to Mrs. Trump stepped forward to defend her relationship with the president. One of them, Hilary Geary Ross, the wife of the commerce secretary Wilbur Ross, said in an interview in early January — days before the news of Ms. Daniels broke — that the Trumps enjoyed a “cozy” relationship.