My Mom went in nursing home in December. Can I transfer her car title?

If you "put $1,800" into the car (repairs?) you MIGHT be able to, possibly, consider that as part of the purchase price toward the fair market value...maybe.
The "use the car" advice is probably the best. Drive her to appts if possible, maybe take her out for an outing --even just a scenic drive if she is interested/able.

talk to an elder law attorney

use/drive car as if it were your own

NO you cannot. Now go talk to her caseworker. They will tell you to buy the car at fair market price and give her the money.

Is your mom on Medicaid? If so, you cannot transfer the title without talking to an elder law attorney as it could disqualify her. If she is not on Medicaid but is within 5 years of needing it, you are in the same situation...it could disqualify her.

Angel