The trips, she said, are chances to teach and to learn from others, yet always with a broader political goal shaped by national politics: to “push the national agenda so that we cannot lose ground, which I feel like we’re doing every day.”

Ms. McCray wears many hats, but she has only one formal city job: chairwoman of the Mayor’s Fund to Advance New York City, a government-controlled nonprofit that raises money to support city programs. Her other jobs, described by City Hall as informal or advisory, include leading the ThriveNYC effort, acting as a chairwoman of both the Commission on Gender Equity and the NYC Domestic Violence Task Force, heading up the Gracie Mansion Conservancy and acting as a member of the NYC Children’s Cabinet.

Ms. McCray resisted the characterization of her multiple roles as informal, although she is not paid for any of them. “I’m highly scheduled,” she said. “I work hard.”

That is also a notion that her husband has pressed recently, insisting that Ms. McCray should be paid for her work, and bristling at the anti-nepotism laws and rules that prevent her from drawing a salary or holding an official position with the city.

“Ask the people who wrote the laws; I don’t understand it,” Mr. de Blasio said. “She works full time. It makes no sense to me. But that’s the reality.”