Both of my parents have dementia and live with me and my fiancé. Can I use their income to purchase a car?

I have POA and I used it to purchase a handicapped accessible van for my mother. I registered it in her name and financed it so that she can write off the vehicle on her taxes for 6 years (on advice of her tax preparer).

My understanding is that if she goes on Medicaid, they will allow her to keep the car because she needs it for transportation.

If I had purchased it with her money but in my name, it would fall under the Medicaid lookback and I would have had to sell it and pay back the money.