I don't want to pay for tickets on a car in my parents name
Why don't you want to pay for the tickets?
They at least have the money.
They might have the money but it is not their fault. It is your responsibility and you should pay. They might not let you borrow the car again if you put it on them.
Fuck them. They make enough money to cover my tickets and they are the ones getting me a good deal on the car.
Don't you think you should own up to the mistakes you make though? It's best to take responsibility if you caused the tickets in the first place.