The car is yours, your name is on the title, and you are insuring it based on you being the driver (not her). You are responsible for parking tickets and toll evasion. Any arrangement you might do must account for these facts.
Legally, you don't have to give her the car, and can report it stolen if she takes it.
Socially, if your family is close enough that you cosign for each other's cars, you need to take family needs into account.
Done wrong, here's an example: Back when there were exemptions, a student could take his own exemption (and save $200 off his taxes) or his parents could take him (and save $1500). The greedy child always wanted the $200, but cost the family $1300 to get it.
Life is hard; it's harder when you're stupid. - US Marines
What I'm saying is, don't be stupid. Take egos and personal greed out of it, and think about/discuss what option will put the family in the best situation overall.
That's what it means to be family. Notice they were there for you: you be there for them. If you are not willing to be there for them, then you should not have asked your mother to co-sign. Cut ties entirely, sell the car and pay it off, get something much more modest, and make your own way in the world. If that doesn't work, well, that's no surprise; people are stronger together.
That said, if you really want to cut ties, come on back here and ask about how to exit the situation where you have a 500's credit score and not $500 in the bank. That is not normal -- well, it's normal for the financially stressed, but it's not healthy at all. As things are, you need them, which means you need to soldier up.