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.
However the issue is goingSome excellent answers to be applying forthis question indicate that obtaining an ESTA. She is supposed to declare all her citizenships in the ESTA application, and declaring a US citizenship will make her unable (which you would need to obtain an ESTA. Not having an ESTA will mean she can't get on a plane. Lying on any kind of immigration application is strongly not recommended, although it's hardfly to imagine what punishment she could be given, since again they can't keep her out of the US.
I don't believe you need an SSN to obtain using a USVWP country passport, so if the 3 weeks delay) is acceptable I would get the passportperfectly 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
Entirely unrelatedly, I hope your daughter is aware that she is legally obliged to file a US tax return every year, and pay US taxes. There has been an increase in people renouncing their US citizenships recently for all of the above reasons.