Hi turbo
With everything you write, it's becoming increasingly clear that your ex is a real danger to you and your DC, and you have to protect yourself and them from him.
The damage he will do to them (and to you) by continuing to be in their lives on this footing must surely be far worse than any damage that his absence from their lives would cause.
He is still abusing you in the way he manipulates you and rewrites the past. He is still abusing them too. I really think that you now have to go down the road of absolutely NO further direct contact with him. If he wants to see the DC, let him go through the legal system, let him contact you through a solicitor. He shouldn't be able to dump his poison on you any more.
Start building your case why he shouldn't be allowed unsupervised access at all, not on Skype or via email either. He is an abuser and he will use that opportunity to mess with their heads as much as he's messed with yours. The fact you have at least some of this stuff logged with the police should surely be of some help here. Is that the police here in the UK, may I ask? I honestly have no idea of the legalities of the situation across borders but you say you're in contact with all the agencies over there so I guess you do have a lot of information.
Were/are you married? Have you started divorce proceedings if so? And are you bringing charges against him? Sorry, don't mean to interrogate you, just trying to get an idea of where you are with all this.
Interesting that your DD's issues could well be related to the trauma, rather than ASD. Yet another reason to keep him well away. And with your older DC (both DS's?) I do think there's an element of Stockholm syndrome in their missing him. Abused children almost always love the abusive parent despite the abuse. It doesn't make it a healthy relationship for them. You started the thread motivated by wanting to do right by them and not deprive them of their relationship with him, but their safety trumps that, surely.
You say you've protected them from a lot of what he did: I think now is the time to start gently telling them the truth, in an age appropriate way. They obviously know some of what he did, given they witnessed the strangling. Yo need to let them know very clearly that what he did was wrong and unacceptable and that you weren't to blame for any of it, any more than they were. Very important that you assign total responsibility for his abuse to him - especially as he conducted such a campaign of making everything your fault, some of that warped abuser's perspective may have filtered through to them and you need to correct it. You know how it's messed with your own head.
Good that your middle DC is accessing some counselling, and sounds like your DD will get support too. What about your DC1? And - what about you? You say you've read the books and the Feeedom Programme, do you mean you've actually participated in it? Whatever the case, I really think you need some longer term support to help you process what has happened to you and to move on healthily. It sounds like you're still only just waking to how bad it really was, and there's a way to go yet. Agree that your new relationship needs to go really, really slowly.
Like mumoftwo said upthread, the fact that he strangled you while you were standing at the top of the stairs holding your baby shows such an utter disregard for your and your DC's safety that you cannot show him any trust at all. And the level of abuse he waged against you - filming the diatribes and the rapes - that's just... Words fail me.
Sorry I'm going on so much! I know that when you're living something on the inside it's very different to hearing about it from the outside. I don't mean to lecture you, just feel very concerned that he still has such access to the DC and though them to you, and that he is using this opportunity to manipulate and abuse you all further.
And once again, you did a really amazing thing in getting yourself and your DC away from him in the first place, after all the years of being worn down like that. You are very strong.