Put your foot down.
No one owes anyone a fucking car.
Kid is no longer a "kid" he is a man grown , he can catch the bus.
He needs some fresh air anyways , will help him learn to take care of things better.
Your wife wants to help him out ? Fine but dont you do it , shes the one that taught him to not be ungrateful and take care of things with elbow grease and hard work.
This is tough love and a lesson for him, you and her.
This type of behavior is makes weak generations