OK, that is a lot of situations... .and there is a lot you can do to improve things. I'm going to start with a general idea that applies to many of those situations:
He launches into circular arguments, long abusive monologues, or criticizes you, either about something happening right now, or he's throwing all the old stuff and the kitchen sink at you. I'm going to lump all this into the category of verbal/emotional abuse.
One of the best tools you have is boundary enforcement, and I almost always recommend starting working on enforcing boundaries against raging / verbal abuse / criticism before you work on other boundaries... .because if you try to enforce another boundary, he is likely to launch into a rage... .so you need to have the tools to deal with that. So it is a great starting point. You can read more about boundary enforcement here:
BOUNDARIES: Upholding our values and independence
BOUNDARIES: Case studies One key thing about boundary enforcement is that it is in the form of "When you do X, I will do Y to protect myself", not in the form of ":)o not do X". In fact, actually telling him you will be enforcing boundaries isn't even needed in many cases. In this case, try this one on for size:
If you start raging/verbal abuse/emotional abuse/criticizing me, I will leave the conversation.
The first action to enforce this can be stating "I will not be spoken to that way."
If he continues, you can leave the room, or if you are on the phone, say good bye and hang up.
If he follows you to the another room, leave the house.
If he blocks you from leaving or follows you, there are more options you can take... .but this is a start. Caring for young children in these situations is another complication... .but this is a start.
While getting the kids ready to go to his mum's place, if he explodes, one response would be "I'm not going to listen to this. I'm leaving right now for a walk. Get the kids ready yourself if you want to take them to your mum's place." And walk out the door and go. I'm assuming that his raging is just at you, and not aimed at the kids... .Don't do this if it would endanger your kids!
Criticism while driving. I personally got criticized for my driving by my wife a lot, and it really triggered me and pissed me off. I'm a good driver; she is an excellent one, better than I am. I found it particularly infuriating that she would directly criticize me, but when her aging father (who had been a good driver when a bit younger) would drive worse, and she never criticized him. Anyhow, this was ongoing, and really touched a nerve in me.
One time (long before I knew anything about BPD or had better tools), I accidentally stumbled onto a pretty good response. We were out somewhere. I got one too many pieces of criticism of my driving. I pulled over, parked, got out of the car, and walked home. It was a few miles. On leaving I probably said something about not being able to take any more.
I'd recommend that you pull over (safely) onto the side of the road or into a parking lot, as soon as you can and state that you will not drive while he is criticizing your driving. And wait for him to apologize or at least indicate that he is done. Same thing about verbal/emotional abuse while driving.
If it is a problem, avoiding being in a car with him may be necessary to keep yourself safe from verbal abuse. It is better if you are driving, because you can pull over and stop, or even get out of the car and walk. If he is driving, you are trapped in the car with him.
Whew, this got kinda long, and I'm pretty sure I didn't get to a few things. Consider it a start, and feel free to ask for more support on anything I missed.