Apologies, i had reached my daily post limit, so could not respond yesterday....
WITHDRAWN - i apologise if it came across this way. I geniuenly thought it was perfectly legal for my daughter and I to enter the US using our UK passports and ESTAs in lieu of a GC and US Passport. I have learned a lot over the past day!
Misrepresnting unintnetionally, again apologies. On the ESTA i stated my daughter was born in the US, was a US citizen and gave her expired US passport number and expiry date and the ESTA was still approved. The fact it was approved naturally made me think what i was doing was correct. I was not trying to pull wool over anyones eyes, i was transparent and provided all the information and it was still authorized. I know now i should never have applied in the first place.
I would like to say i have learnt a lot and now understand my daughter should enter on her US passport, and I on my GC and then sign a I-407 in exchange to be able to stay as a visitor for my scheduled 2 week visit (i have always planned to abandon). I hold my hands up and say yes i was undeducated and ill informed, you don't know what you don't know and when both ESTAs were authorized i assumed i had done everything correctly but yes i should have researched earler! I have now been corrected and understand for the future! I hope at least this is a good warning to others.
As i said i will enter with my GC and be transparent with my situation. I have an appointment booked next week (earliest possible) at the US embassy in London to get a US passport for my daughter, this will have to be an emergency / expedited one as we leave 8 days after the appointment, keep your fingers crossed.
One final question please: My ex-wife / daughters mother (who we are fluing over to visit) can't attend so is going to sign a DS-3053 consent form, have it notorised and send to me along with a copy of her ID. Can the form be a photocopy? I.e. scanned and emailed to me? Or does it have to be the original? I see nothing online explicilty stating it has to be the original? She is going to scan and email but also send via Fed-Ex on the quickest delivery possible, but just want to know my options incase it doesn't arrive in time.
Thanks again for all the advice, perhaps i will sort all this out just in time. Lesson learned!