Sorry, not going to work.
Unfortunately, TN has a very low homestead exemption, under $20,000, so quitclaiming the home to beat the judgments would be a fraudulent conveyance and could be undone by the court.
Paying off the $100,000 releases one debt but still leaves the $900,000 debt (is that right? 5 zeros?) and the equity in the home would have to be used to pay that down before your mother could file bankruptcy.
The kind of lawyer your parents need to see is a bankruptcy lawyer to see if there is any hope at all of keeping the house.

