yep. have her go to the bank and refi it in her name only. If you need to pay a few thousand to make it happen, do it. It will be cheap for you in the long run.Anyway, back to the OP, being a co-signer does not automatically make you co-owner. Ask anyone who ever cosigned for their kid and the kid defaulted,
BUT for adults, it usually is the case that both are co-owners of the vehicle. Likewise, they are both owners of the indebtedness, meaning both are liable for the full amount of the indebtedness. Who get the car and who gets the debt are decided by the parties in the divorce proceedings, (or the court). BUT, AND THIS IS REALLY REALLY IMPORTANT = that agreement is NOT binding on the creditor. Meaning if she agrees to pay the loan off, and defaults, the creditor can come after you for the entire balance. Cry all you want "she agreed to pay it" and the creditor will tell you it doesn't care.
The only way to completely deal with the debt is to pay off the loan and refinance, or get the creditor to release one of the parties, which is very unlikely.
Having said that, you probably have a lot more unknown debt hung over your head that you don't even know about yet. I hope you don't, but you really ought to be expecting it.