I disagree about heading to the courthouse UNLESS that's what you guys really want to do, for the following reason:
Your FMIL is a toddler. She's throwing a fit, and if you give in, you're just going to have more and more fits to deal with, because she'll have learned she can get her way if she gets nasty enough. (Also, as I'm sure you know, your financial aid packages will change *dramatically* once the 2 of you combine households legally... BESIDES it's your lives, you deserve to wed the way that YOU TWO want to wed.)
Again, since she's acting like a toddler, I would recommend treating her like one. She's on "timeout" and you will have nothing to do with her until she composes herself. You can't send her to her room, but you CAN do the equivalent, which is to refuse to interact with her. Don't have her over to your house unless she can be nice, and if she starts being mean tell her she has to leave. The whole "you don't have to go home, but you can't stay here". Ditto if you're somewhere else with her around (even thanksgiving dinner, and she starts being mean... give hugs all around to others, and leave). Your fiance can go see her anywhere ELSE but your home... don't try to cut off that relationship... but until she stops bullying and throwing tantrums, just refuse to have any contact with her. Your F will have to be on board with this plan, however, or it won't work. Just like parents of a toddler. If one parent is consistent, and the other gives into whining... you've got a whining child.
And ditto the cosigner thing. I realize it's probably merely one example amongst many... but she has no rights to the car. The ONLY right she has to it is if your F quit paying, she has the obligation to pay or be sued by the company that holds the loan.
Which brings us around to step 2. Cut any and all financial assistance from his mother. If any is coming from his family, have it come from his father... but even then, that still leaves strings. She only has as much power over you 2 as you let her.