Yes, and yes. You can take out a reverse mortgage, and you can get reimbursed from the mortgage for money you advance for repairs to the house. However, be very careful to document every dollar that you spend. The best approach is to lend the money to your mother and have her sign a promissory note memorializing the loan and then have her pay for the repairs herself. Otherwise, the Medicaid agency might view your payments as a gift to your mother and her reimbursement of you to be a disqualifying transfer.
Finally, with respect to the remaining reverse mortgage funds available to be drawn on when your mother moves to the nursing home, confirm with your state Medicaid agency that they don’t view these as available to your mother. They shouldn’t, but with 51 separate Medicaid programs out there, it’s best to confirm that they don’t.