Thanks for all the responses, a couple of responses.
We applied for an ESTA and it was denied, so now she has an ESTA refusal on her record, I’m sure that isn’t good.
We have no intention to permanently relocate to the US for the foreseeable future, we just want to visit occasionally.
We decided to go ahead and book the flights but as a precaution we chose JFK as the port of entry only because it’s the easiest place to return to the UK from should the worst happen. To be honest it feels very strange to be worrying about potential deportation while in possession of a valid GC when countless thousands of Brits pay £21 online for an ESTA and off they go. But here we are 😬