OP, just another idea for consideration....
So the children enter visa exempt on USA pp.
That 30 day stamp can be extended by 30 days if required.
During this time she can obtain for them a Thai ID and subsequent Thai passports.
BTW: my Thai partner just recently obtained new pp.
Turn around was 2days.
Granted with the Thai ID etc for the children will be much longer but possible.
There is a recent thread with similar suggestion.
She might then need to do a border bounce to close off the entry/exit on their USA pp.
Yes messy however this paves wave for living in Thailand as Thai citizens.
Their USA pp are intact and can return to that country at any time.