Ex-wife was awarded the her car in the divorce, hasn't refinanced so my name is on it, and she defaulting by $772.80.

File a motion to enforce the decree, ask the judge to appoint a receiver to sell her car and pay off the note. You will need an attorney to help.

Going through a divorce in McKinney Texas

The mortgage company will go after you, the debtor. The county may go after you both since your names are on the title. She can just move out. ...

You should be fine without the VINs. It would be best to get and write them in the Decree, but it won't stop the judge from signing it.