My mom is always trying to give us gifts. For examples, my van was too high for her to get into so she wanted to buy me a car. I let her pay for half. The car is also easier for me to put her wheel chair in ( and get it out) since I am 63. I have no documentation that the $5,000 was her gift. Do I need some?
If she is permitted to have a vehicle of any value, and the title to the vehicle is not currently in her name, transfer the title to her. Alternatively, you can give the gift "back" and then have her purchase the car from you. Document everything.
If you are contemplating applying for Medicaid for her then you must deal with this because a $15,000 gift (are there other gifts?) will cause the implementation of a penalty period of ineligibility.
Going forward, always use your mother's money to pay for her purchases. It is just so much easier that way when it comes to application time.
Though an interesting thought, it is unlikely that a "normal" car not fitted with special devices will qualify as "medical expense". In any event, the deduction would not apply to you unless you are responsible for at least 50% of your mother's support. It is similarly unlikely that if the vehicle so qualified your mother would be able to take advantage of any deduction in that she is probably paying little or no income tax as it is.
The only glitch might be if the car is registered in your name. And I do not now how the Medicaid people would view it. I guess you could point out that your mother purchased half the car for her needs and you purchased the other half for her. (you may want to consult a tax attorney, if she is a dependent there may be a tax deduction for your part of the purchase)
btw, why did you not want her to know about the real price of the car and that it is really for her needs? She should probably know that in case she is questioned about it.
good luck