One symptom of Alzheimer's Disease is thinking that others are plotting or scheming against you. He probably feels like you are "out to get him" and are trying to take away his independence. Take the car away, and hide the keys to your vehicles. If your father asks about the car, insist that it is away for repairs. Volunteer to drive your dad where it is he needs to go. It may hurt to tell your dad these tall tales, but it would be even worse if he got on the road and hurt himself or someone else.
I'm sorry you have to be in this situation, but just remember that if there is no car, there is no driving.