You signed knowing the obligations that you would incur. If they decide to pursue reimbursement from you, you should expect to be held responsible and make payments. You should have planned on this possibility before sponsoring her or having children which you cannot now afford to support. Your mothers care is not my responsibility; it is yours. I am strained paying for my disabled child who is a native born citizen yet gets no benefits from the state.
It is a fact that is tracked in my state that citizens without health insurance yet make too much to qualify for Medicaid die every year due to lack of medical care. It is an unfortunate fact of life that medical care is rationed according to ability to pay.
Your mother could have return to her native country and received treatment there. Since she did not, you must abided by US laws and your contractual obligations.

