Neither your parents' reverse mortgage nor their spending of the money from the mortgage should affect your mother's eligibility for Medicaid. When Medicaid decides on eligibility, it looks at an
individual's, or in this case both your parents', income and assets, which have to be very low. In most states, a couple's cash or other liquid assets cannot be more than about $3,000. But the good news for your mother is that when deciding eligibility, the value of a house the applicant lives in is "exempt" -- meaning Medicaid does NOT count the value of your parents' house when considering how much in assets they have. That also means that Medicaid will not count any of the money your parents have spent on fixing up the house.
The same rule applies to your parents' car, which is also considered exempt from the Medicaid assets limit. In some states, though, the exemption for a car has a limit on it, usually around $5,000. (That means that having a new car worth $15,000, for example, could put someone over the asset limit.) If your parents have a used car, it's less likely that it would disqualify your mother from Medicaid, but be aware that if the car is a fairly new one and its current market value is over their state's limit on exempt vehicles, your parents may be forced to sell that car and get a cheaper one, using the money they get to pay for other necessities, after which your mother would be eligible for Medicaid.
To find out more about the Medicaid eligibility rules in your parents' state, including whether there's a limit on the value of a car, you can go online to any search engine and enter "Medicaid" and the name of the state. Or, you can call the Eldercare Locator toll-free at 800-677-1116 and ask them for contact information to the Medicaid program for your state.