@Jen I hadn't visited the forum in a while, so I only read about this after it is all over, but I want to add my opinion anyway. I agree with @Amira that your mother's action was not OK, and that to me it sounds like she is trying to get more control again. Now that she has succeeded, I would guess she will try again, so my advice would be not to get too attached to the car: there might come a time where she wants something you really don't want, and you need to feel free to say no then.
I wonder if she deliberately proposed it to you that late, so you would have little time to get your thoughts organized. In any case I think it was a disrespectful move from her part, and risking the good understanding about the belt you had going.
In the end it seems to have worked out OK, and you might even feel the net result was positive, with the adaptations you worked out, but it was still a one-sided breach of your unspoken agreement that you decide when the belt is worn. (Yes, you were not literally forced to wear it, but depending on your actual situation, the use of a car can be close to a necessity.)
