As someone who went through the same I can tell you you're being given great advice here. The less contact you have, the better. It's incredibly hard when it's the person you thought was your other half for so many years, but it gets easier.
It's very early days for you and you'll be up and down. It's natural. What you're going through is, in my opinion, harder than a bereavement. When someone dies you can at least enjoy the happy memories and know they didn't choose to do this to you. In your case, it may feel that your past is tainted, and you know he did choose this. But time is the great healer that everyone tells you it is: not tomorrow or next week, but you will feel better, and one day you'll surprise yourself by waking up feeling fine...or even happy!
Don't despair about your house. Under the circumstances you may be able to hold onto it for at least a few years so that you don't lose too much. And by then you might be ready to move on and find somewhere for yourself and the kids.
One piece of advice I would give you: don't be lured into the "ex-wives club". There was one of these where I worked and they loved a new member who they could "comfort" with their all-men-are-evil beliefs. It's not helpful and doesn't really help you move on, just leaves you old, lonely and bitter. Everyone was surprised when my lovely, supportive husband turned into a cheating, lying, selfish man who didn't even care about his children any more, and it would have been so easy to join that club. I thought my life was as good as over. But guess what? I'm remarried, to the loveliest, funniest, most considerate man I've ever known, who 2 out of my 3 adult children now regard as their father, and is the grandfather to their children. My ex? He only sees 1 out of 3 of his children and hasn't even met any of his grandchildren. I imagine that hurts, but you reap what you sow.
One last thing...remember, he's not your friend right now. Take everything he says with a pinch (or handful) of salt, check "facts" he's given you re legalities and get what you need, not what he wants you to have. Your children (and you) need and deserve a decent home. If that means he has to rent a cheap room in a shared house, tough. He should have thought about that before.