Call and make an appt at your local social security office with your mother and ask to talk to a social worker about your mother’s health condition and homelessness.
They can refer you to local homeless shelters and programs for elderly homeless people. Your mother should be eligible for Medicare and/or Medicaid to pay for her medical care. It is very painful to reunite with an abusive parent, try to find a support group or someone you can confide in to help you through these feelings. If you are contacted by a social service agency, explain to them your situation. In some states, there are filial support laws that obligate the child to pay for the basic necessities like food and housing, check to see if those laws exist in your state.