So sorry to hear all of this!
Although my ex and I generally get along very well, every few years I unintentionally press his button about something and he will lash out with the most ridiculous, distorted, exaggerated accusations, making it sound like I'm a bad parent. After a good chunk of time, I always realize that what I said had made him feel terribly insecure and he was just childishly throwing up whatever defenses crossed his mind, to avoid thinking too deeply about the thing that made him insecure and to shift my focus from the uncomfortable subject, to defending myself. And boy, does it work! In the moment - and typically for several days afterward - I feel terrible! Also, the more upset, surprised, defensive and emotional I get, the more calm he becomes - even while saying nasty, ridiculous things - and he will keep pointing out this difference, as though it's mutually understood that being icy automatically makes him right and being emotional automatically makes me wrong. Which is infuriating, when what he's saying is so obviously wrong and specifically intended to be upsetting.
I understand the aversion to putting yourself through that - especially if you know beforehand what's coming. It sounds like you should strictly limit yourself to written communication with your ex. You can take the time to phrase your own position carefully and then just leave his responses in your Inbox, until you feel ready to skim over them. Try to approach them like a foreign language translation. Not that you want your daughter to fight all the battles for you - you should protect her, more than she protects you - but since she's going to get sucked into some battles, when she's with her dad, you should train her to "do translation", too.
"Let's focus on how screwed up your mother is, with her anxiety, nervousness and anger
" translates into, "I don't have a good answer to what you're saying about the seat belts. If I upset you, maybe you'll quit talking about them? Also, I feel criticized - I don't want to admit that the criticism is valid - so I will change the subject and criticize someone else."
"You must not like your step-sister, then
" translates into, "I'm limited, in my ability to motivate people. It upsets me, that I can't figure out how to help my daughter make more friends or enjoy school more. I hoped you going to school with her would be a magic cure - even though, obviously, fixing your step-sister's social problems is not your job. I don't know how to handle my disappointment, that you won't do it. The only (childish) tool I have in my toolbox, to try to convince you to change your mind, is guilt. Obviously, I think you're a good-hearted person, or guilt wouldn't make you second-guess yourself."
"I'm compiling a list of the kids' complaints about you, and exaggerating them. Eventually, I'll wind up with custody
" translates into, "I'm afraid the kids complain to you, about me. I'm afraid you have it more together, as a parent, than I do. I'm afraid you have enough ammunition to get my parenting time reduced, or make the kids hate me, or cause problems for me in my new
family by cracking down about my unpaid child support. Your very existence - your competence as a parent, your control over the kids' lives, your ability to move on and not mourn the loss of me - makes me feel totally insecure. I have zero adult resources for handling such fear and insecurity, so I just get angry at you for causing it and try to get back at you, as though if I can make you fearful and insecure it'll lessen my own feelings. But I'm sure that the only way I could ever take custody from you is if you did something drastic and crazy, like poisoning the kids. That's
why I never criticize you about anything reasonable
You might consult someone about the possibility of getting supervised visitation? I'm not saying that's warranted. I'm only reading a few paragraphs you've written on a message board. But if your kids are consistently upset by disregard for their privacy (showering with their dad past the age when it makes them uncomfortable) and manipulation - and your daughter, at least, is willing to take a stand about it - perhaps you could make an argument for them spending time with their dad in public places, with a chaperone who could intervene, if grossly inappropriate things are said to them. Your ex and his wife would quickly learn to control what they say, so it's not overheard - and this would necessarily make them conscious of the inappropriateness of some of the things they were accustomed to saying, before.