OP, this is horrific. On lots of levels. Also, I'm guessing that he's training you never to challenge or disagree with him because you are worrying that if you do, he'll give you the silent treatment for a week or more?
Also, I assume it only stops once you've sufficiently prostrated yourself and begged forgiveness even if you didn't do anything you felt was wrong?
To take some time to calm down is fine. If someone has done something truly awful and you're struggling to process it, I can understand how that might make normal life a bit tricky. But that doesn't mean you get to check out completely and certainly it doesn't mean that you simply decide you're not involved with family life.
i'm not sure what, if any, answer there is here for a happy resolution but I'd be telling him that if he wants to do the silent treatment, that's fine, but you will no longer be tip toeing around it or accommodating it. So go about your life, do NOTHING you wouldn't normally do, if he won't engage, don't engage bak so no cooking, cleaning etc for him. Also, he will be expected to do the same childcare stuff as he would normally and then get on with it.
But I'm not hugely optimistic and I think there'll come a point where it will be easier to just to walk away because this man is clearly not a nice person.