I don't know what kind of laws...that is why I am on this forum. It just seems there would some issue with a car loan being initiated with a hand written peice of paper.
Well, actuslly no. That is what is often referred to as a written contract or agreement. So much easier to prove and enforce to a verbal agreement or contract. It being handwritten actuslly strengthens the agreement as the writing is evidence of at least one of the parties involved and the style and form can be used to show a lack of duress.
Anything else you have that might strengthen the case against you?
The HUGE issue you have is the agreement to pay may be inextricably intertwined with the other issues within the divorce agreement that invalidating that requirement could create unsolvable issues regarding other matters within the decree.
An example would be that in exchange for you paying for the car the ex allowed you to keep something. First, it is near impossible unless specified as an actual tit for tat exchange to identify what you recieved in exchange for you agreeing to pay for the car. The decree is taken as a whole. You are attempting to parse it into individual elements. That may not be possible.
I would suggest you consider what you are willing to offer in exchange for the voiding of the requirement to pay for the car. It is inequitable to demand you benefit from a change without equal consideration afforded the other party.