Ms. Chao’s office had made a series of unorthodox requests related to her first scheduled visit to China as a Trump cabinet member, according to people with knowledge of the email. Among them: asking federal officials to help coordinate travel arrangements for at least one family member and include relatives in meetings with government officials.

In China, the Chaos are no ordinary family. They run an American shipping company with deep ties to the economic and political elite in China, where most of the company’s business is centered. The trip was abruptly canceled by Ms. Chao after the ethics question was referred to officials in the State and Transportation Departments and, separately, after The New York Times and others made inquiries about her itinerary and companions.

“She had these relatives who were fairly wealthy and connected to the shipping industry,” said a State Department official who was involved in deliberations over the visit. “Their business interests were potentially affected by meetings.”