You have to learn to accept that your h is a selfish, spoiled brat at the moment. I do understand the situation, but nothing is going to change when it comes to his way of thinking, so you need to accept that and move on from there and figure out ways to think outside the box. I would be looking for Plan B's when it comes to taking care of you and your children. You can't rely on him to do the rational thing when all he's thinking about is himself.
When he sees/senses that you are doing things differently, he just might come around a bit. The more you attempt to talk to him about splitting things, including the time w/the car, the more he's going to find ways to aggravate the "snot" out of you. He enjoys the fact that you have to ask/beg from him. Stop doing that...you aren't dealing w/someone who cares one fig about you and evidently not the children either...unless he thinks he'll get more out of having custody of them. Unfortunately, to him you come off as a whining shew that wants her pound of flesh from him. Show this man you can be that independent woman wjo doesn't need to rely on him. The more you appear to whine, the more he'll dig his heels in.
Gerda, you are a smart woman...please stop trying to rationalize w/him...you can't win him over and neither will the lawyers. When something isn't working, try something else. I've given you a simple suggestion to try. When a person puts the ball in someone's court and gives them opportunity to actually think about it and they have a choice to say yes or no, they sometimes will say yes.
In the world of MLCers, it is either black or white...no grey area at all. Try something different next time. Don't be afraid to try something different/new.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.