So much of this is triggering to my experience.
hellsbellemelons (as always) has given you some excellent advice. You are going to need to start setting some boundaries with your ex. You are going to feel uncomfortable setting them but you need to do it. Don't be afraid to ignore him, tell him to speak to your solicitor. He'll try and push all your buttons with the charm, pity and rage channels when he realises he is losing control of the situation. He's playing exactly from the cheaters hand book...same old cliches...listen to what people are telling you, we've been through it.
You're doing great so far, do everything through your solicitor, disengage from him. I made some terrible mistakes in the beginning, played along with the narrative of being friends and not using solicitors at the request of my ex. He isn't your friend, friends don't do this shit, let alone someone you are married to and have children and a home with.
As others have said don't be ashamed, you've done nothing wrong. Don't vent on social media, but don't hold back from telling his family everything he has done. He's an absolute dickhead! a self entitled, narcissistic, selfish dickhead.
Probably the last thing you want to do right now is read a book, but there is a book that saved my sanity and maybe even my life when I was going through my hell...
leave a cheater, gain a life by Tracy schorn
www.chumplady.com/book/
She also has an excellent blog, it's mainly American but there are British people on there too that can offer you virtual support. Be wary of who you vent to, as nice as his best mate sounds what you tell him will no doubt get back to your ex. I found one good friend who had been through the same as me and vented to them. They were great and said i could call, text, visit any time of day. Tell your family if you haven't already, mine were great.
Good luck OP x