A dual US-UK citizen in the US will always use the US passport for entrance and UK passport for “exit”. The government is smart enough that the two passports are connected.

Thank you, yes this is exactly the dilemma..because she is starting her return journey from Mexico flying via the U.S. back to the U.K., she will need to use her U.S. passport to in the airline system to prove she can enter the U.S. but the system will flag that she needs an ETA thinking she is only a U.S. citizen and so she will need to go to the airline counter in Mexico and show them her U.K. passport to demonstrate she can enter the end destination of the U.K. without need for an ETA. I think this is the consensus everyone but please correct me if I am wrong.