Badger, sounds like a difficult situation. I will share a few ideas that helped me with similar issues.

If there is anything positive that you and your mother share, it helps to focus on that. I simply refused to take part in negative or silly conversations like the one your describe about your car. Abruptly changing the subject or calmly leaving the room eventually had some some effect.

Also -- an "old person car"? What on earth does that mean? I'd be tempted to giggle about that and ask for more details. Maybe grab a pencil and paper and start taking notes -- which is thoroughly obnoxious but I did it once and it was fun.

Enjoy your new car -- doesn't matter what anyone else thinks.