Emergency travel to USA ...passport issue

Hi all, my US husband lives in the UK with myself (UK) and our two dual citizen daughters. Both their US passports expired around Easter - the plan was to make the appointment at the embassy over the easter break to renew them, unfortunately lockdown put a stop to this. During lockdown my father in law has passed away in the USA and my husband needs to travel over to support his mum. My eldest daughter is 16 and she was going to go along too, to support my husband and her Grandma (I am assuming I won't be allowed in as a UK citizen). They are hoping to go over mid-July.... the problem is we haven't been able to renew her US passport as the Embassy not processing renewals, we don't want to book flights in case it isn't possible. She has a full UK passport. We have continued to try and contact the embassy by phone and email but not had a response. I know she should use a US passport but in the current circumstances is it possible to fly with her dad on her UK passport. If not we need to get an emergency passport but don't want to book flights in next 7 days until we know she can get a passport.
Any help much appreciated.
Thanks
Rachael

She will be granted an emergency passport with the flight booking. Not an issue.

And you can travel to the USA, as your the spouse and parent of US citizens.

I’m very sorry for your family’s loss.

Thanks - we are really worried about booking the flight and then not being able to get an appointment for the emergency passport within the seven days. Also, I read that if my daughter is 16 just one parent can go to this appointment. We live in Manchester and have a high needs 6 year old so would be much better if just my husband and 16 year old daughter can go down. Are the emergency passports always in person in London? Thanks so much.

Also, would it be then possible for us all to travel to the USA, even me (as British citizen)? Are there quarantine restrictions when in USA? Thanks