She needs to send her mom this letter: Dear Mom, I appreciate what you have done for me in the past and I hope that in the future we can be friends again. But by not allowing me to be totally responsible for the insurance on my car, you may be putting yourself into finanicial peril. As a registered owner of an unlicensed vehicle, state laws could make you held responsible for any and all costs if the vehicle is involved in an auto accident. These costs can run into the hundreds of thousands of dollars and innocent people have lost their homes and careers because of the actions of others. Also, the creditor financing the vehicle requires that the vehicle have insurance or they will repossess the vehicle and both of us will receive negative marks on our credit reports. Despite the difference of opinion we are having at this time, I hope that you understand that I am looking out for you welfare by taking full responsibility for maintaining insurance on the vehicle. Thank you, your daughter.
A couple of points. As the car is still being financed, your girlfriend and her mothers name are not on the title, just the registration. Who ever is financing the vehicle is the legal owner and only their name is on the title. And the financing party most likely has a requirement that full coverage insurance be maintained on the vehicle or they can do one of two things. They can put their own insurance on the car but this insurance only covers them, not your girlfriend. She would still technically be uninsured. The insurance would not cover her if she is in an accident. Or worse, they can repossess the car and sell it at auction. Your girlfriend and her mother would still be required to pay the difference between what was owed and what the car sold for. And both will receive negative marks on their credit reports.