Yes, the transaction you describe will work. If you can substantiate the fair market value, Medicaid will not penalize the sale. As part of the process, you will have to pay off the reverse mortgage. Your mother will receive the $50,000 differential between the reverse mortgage and the fair market value. And she can pay you fair market rent, which you will also have to substantiate. The question you will have to consider is what happens when your mother runs through the $50,000 and has no more money to pay you or her other expenses.
For more information about Medicaid planning.