_norbert

Unfortunately I don’t believe that “has a sole or surviving parent who is unable to care for the child, consistent with the local standards of the foreign sending country, and who has, in writing, irrevocably released the child for emigration and adoption” is as simple as saying  “she can’t take care of them because my parents are paying”, or something like that. You’d probably need some kind of court finding that she is either mentally or physically  incapable or grossly negligent in looking after them. And as above, as it would be a non-Hague adoption it wouldn’t work for immigration purposes either. It’s a sad situation. 
 
I’m assuming that the boys themselves have no claim to being USCs or that would be first option to use?

A Hague Convention adoption does not require the adopting parent to reside with the child abroad.
 
With a private and non-Hague adoption, the 2 years residing with the adopted child abroad is required.
 
You are operating under the flawed logic that all adoptions are the same.  They are not.  Different types of adoptions have different requirements.