Can my mother sell her old car on contract to me with payments that won't put her over her medicaid asset limit of $2000 per month?

No, and the reason why is because she has Dementia, she is not competent to enter into any contract. If you are her POA you can sell it and it must sell at market value. If you don't have POA, nothing u can do. Under Medicaid, Moms car and home are exempt assets until death.

You may want to consult with an elder lawyer to see what you can and can't do.

Yes, you can arrange payments in this manner. But do this legally through an attorney so that this cannot be questioned. And be certain to buy her car at fair market value with stipulated monthly payments PLUS INTEREST as anything else is gifting. I recently found this out through my CPA when considering whether or not to make a loan free of interest to a loved one.