@Thecrocodilewhodidntlikewater I was hoping that not ALL of my guesses would be right.
I don't want be a scaremonger, but at this point I think you need to be very careful. The good news is that it sounds like to any rational person, it's clear he's NOT being rational. The fact that your friends are remaining "your" friends is good - these sort of men can be surprisingly good at alienating you from even your own family or friends, but they can often go too far and the wool falls from everyone's eyes (my favourite being the man who rang up his ex's friend to scream at her because he had not been invited to her 50th. The bizarre bit is that afterwards, he couldn't understand why, once he'd "explained" it to her, she still didn't send an invite...)
Nonetheless, you need to be on the lookout for him to start threatening you and use any small perceived weakness against you and/or to blatantly lie. You're a bad mother. You are drunk all the time. You shout at the kids. You are working and he is doing all the childcare. On that vein, be prepared for him to threaten to take the DC from you.
As much as possible, it's grey rock time. Don't engage, don't argue, don't debate. Accept that he is irrational and that nothing you say or do will change his mind. Be prepared to pick up the slack once he starts using the DC to punish you by being unreliable, flakey etc.
I assume you own the house which is why you can't just kick him out? Does your solicitor have experience in dealing with divorce in the case of emotionally abusive men? I believe - but don't know details - there are things that can be done to try speed things up in that case.
Mediation is unlikely to go well. He's already expecting to be told that HE is right and YOU are wrong. Unfortunately, this sort of delusional thinking means he won't engage with the mediation process and might even come out of it thinking that x happened when everyone else can see that it was y.