So sorry, this board doesn't get a lot of activity and it's been awhile since I've been on.
Verbal abuse is subjective. According to the namby-pamby, bleeding heart, politically correct crowd not sharing your thoughts/feelings is 'verbal abuse', forgetting an important event is 'verbal abuse', not wanting to beat a dead horse or agreeing to disagree is 'verbal abuse', saying anything negative about someone is 'verbal abuse', judging or criticizing is 'verbal abuse', any form of ordering is 'verbal abuse'. As such, there isn't a single person on this planet who isn't guilty of 'verbal abuse'.
Also subjective is a legal definition..."the repeated improper and excessive use of language to humiliate or undermine someone’s dignity." How do you define 'improper'? I know folks who use the word 'f**k' all the time...to them, it's just a word like any other word. Is it 'verbal abuse' to tell someone who acts like an ass frequently that they are an ass when they act like it?
In the situation that you describe, "ex said that he says things when he gets upset but was just joking and that the kids know he is joking", it is less a straight 'verbal abuse' issue and more an 'anger management' issue. Sure, he may not mean what he says and the kids know that he doesn't mean it, but it gets really old and hurtful after a while.
And that is how I would explain it to your ex and her boyfriend. There is nothing wrong with getting angry, upset and/or frustrated, but it needs to be constructive...not destructive. Trivializing his lack of control is demeaning and insulting...it is teaching the kids that they can say whatever they want no matter how bad so long as call it a 'joke'.
As to your other issues:
Grandparents - There is nothing you can legally do about the grandparents except on your own time. When you have the kids, invite your parents and your former in-laws over to spend time with the children or let the kids go over there. If your ex says anything, tell her that she has no right to deny the children access to their grandparents so long as the children are not in any physical danger and ice and cake for breakfast has never killed anyone.
Transportation - Assuming here that you're supposed to split it...one picks up, one delivers. Simple solution...next time you pick up the kids, you don't take them back. NOT saying you 'keep' the kids...just that barring any emergency situation...she is supposed to pick them up and if she refuses, they stay until she does. And if she tries to deny you access to the kids because of it, you contact your attorney and put a stop to it.
If you air your dirty linen in public, expect people to comment on the skid marks!