[hocus pocus]

I'm sorry to hear about this, you must be frustrated! You mentioned that your grandmother said she'd co-sign for a car and that shows that she believes in your driving abilities. Perhaps you can see if she would be willing to talk to your mom about this. I think you may benefit from mentioning the fact that you're helping in payments toward the car. You could tell your mom that you understand it's your family's only car, but you're helping to pay for gas and you'd like to be able to venture out on your own. You might be able to tell her that your driving skills will improve even more if she lets you out on your own as that's something a lot of new drivers struggle with.