Can dual US/UK citizen travel with only UK passport and ESTA? [duplicate]

US law says that a US citizen must use a US passport to enter the US. However US law also says that a US citizen cannot be denied entry to the US.

If she makes it to the US border, the most likely scenario is that if they discover that your daughter is a US citizen, she will be given a short lecture from the immigration officer about how she is supposed to have a US passport, before they admit her anyway. That's annoying but nothing more.

Some excellent answers to this question indicate that obtaining an ESTA (which you would need to fly to the US using a VWP country passport) is perfectly possible, even declaring your American citizenship. As an alternative, if you can fly in to Canada or Mexico you could then cross the US border without needing an ESTA.

She could fly to Canada and enter the US by land. To enter Canada, she can use her US birth certificate, meaning she won't even need to pay for an eTA (if she doesn't have the birth certificate on her, of course she can use her British passport with an eTA too)

The alternative would be applying for an ESTA on her British passport, however she should deny holding dual nationality, or the ESTA may be refused. I also can't guarantee that the system won't find out about her US citizenship.

The US government used to have a page that read, in part:

If you have a true emergency, and are unable to obtain a U.S. Passport before your travels, and only have a VWP-eligible passport, then you will have to apply through ESTA using that passport to travel to the U.S. When arriving at the U.S. airport using the foreign passport, you will have to use the non-resident queue.

However, that page is no longer available. The proper course of action for your situation is probably to apply for an emergency passport.