Mathimatically you are nearly correct. She put in 2900 (2000 plus 3 years insurance) and you 1500 so she roughly owns twice what you do. To make a hundred percent, then she owns 66.6% and you 33.3% so 33.3% of 2000 is $666.00. So if I've done this correctly, asking for $500 is a deal for her! But, if she maintained the car and if she had to pay any other costs, those need to be deducted.

This is also assuming that you were reliable with the car and didn't cause undue worry or frustration for her. You were trying to help each other almost as friends. I would never treat my daughter like this. I would have given you the car when I received the gift from my mother. Sorry, sounds like you didn't do too well in the parent department.