I understand this mother not wanting to abandoned her child...but you do have provide a guardian (paperwork, names, phone numbers, power of attorney etc) for your children in case you are deployed. It has been this way since the first Gulf War.
And so what happens when the guardian bails out?
I wonder there a way sound like both US Miltary mostly Civilan social system fail this poor lady
Either that or apply for a hardship discharge.