@BookishBabe
Wow! You are really being put through the mill!
FWIW here's my two cents (in no particular order)
His mental health is no longer your problem. Drop that rope. If you think 'getting help' going to magically restore him and restore your marriage, it won't. Not all people with mental health issues cheat, and not all cheaters have mental health issues. He is simply who he is. Besides, he hasn't been diagnosed with anything, other than being a magnificent arsehole.
As far as why why why did he do this, you know, I've found that it really doesn't matter, it doesn't lessen the pain, and it won't change anything. So instead of focusing on 'why', focus on 'what next for me'. Which leads me to......
See a solicitor. Doing so doesn't mean you're going to 'do anything'. It just means you're educating yourself as to what the coming divorce may mean to you and DC. Whether you have gazillions or diddly squat, there will be legalities involved with the divorce that's soon coming. Take a 'snapshot' of your family finances, income/outgo, account balances, etc and show it to the solicitor. They'll be able to give you some idea of what you may be able to expect. They'll also be able to tell you what is 'likely' as far as child arrangements and maintenance. Chances are he isn't going to want 50/50 as that will interfere with his 'new life', but you need to figure out what will work best for you.
As far as your job, as long as you know the children will be safe, you need to bite the bullet as far as them being around OW. I know, it hurts. But you have to think long term, not just 'tomorrow'. And long term, keeping your job is important. You want to be as self supporting as you can.
So, you still love him. That's to be expected. Don't try to deny it that only makes it take longer to 'get over'. Accept it and say "Yes, I still love the sonofabitch, but I won't always. It will pass in time". When 'those feelings' come, don't wallow. Instead just let them roll over you like a wave. If you've ever swum in the ocean you know that fighting the waves does no good. But if you relax and just keep your head above water, eventually the wave dissipates and you can swim safely to shore.
It's important to keep your dignity. That's the part about not doing the pick me dance and trying like hell not to cry or show emotion in front of him. Don't show visible anger. React calmly and cooly no matter what the provocation. Remember the phrases "That's your opinion", "I'll have to think about that", "I'll get back to you on that", and "I'll have to discuss that with my solicitor". They'll cover just about every situations. Oh and the MN famous "That doesn't work for me".
You wonder why he's being so nasty? I have found that men who leave their families because of their dicks often are. They want you to gaily wave them off without a scene, so it angers them when you get upset. But then when you manage to be calm and cool they get angry that you aren't falling to pieces over 'losing them'. Can't win for losing, can we? Assholes.
The most important thing is to put yourself first, take care of yourself first. In doing so, you will also put your children first because having a healthy, calm (and eventually happy) mum is the best gift you can give them.
You'll get through this. You really will. It's a marathon, not a sprint.