First of all, the New York exemption for a homestead is $50,000. That applies to the equity
in the homestead as opposed to the amount of the debt owed. Ie. if the place is worth $80,000, then the first $50,000 in equity is protected.
Its not common for a creditor to try to do a forced sale of a home for a debt this small. A forced sale can cost the creditor 4 to 5 thousand in attorneys fees to pursue. What they would most likely do is just record a judgment lien on the property and wait for it to sell.
One option for the mother to consider would be to file a Chapter 7
or Chapter 13 Bankruptcy. This could potentially eliminate all of the credit card debt
and stop the lawsuit dead in its tracks. She could keep her home in a Chapter 13, but would have to propose a partial repayment plan
to buy back the nonexempt equity.
She may be able to do a Chapter 7 depending on how, exactly, much the home was worth. If it was worth say $50,000, or maybe even $60,000 she might be able to do a Chapter 7 bankruptcy to eliminate all of the credit card debt and still keep the home.