I feel like telling everybody to CALM DOWN please.
O.k. Ants, I think you have to take a deep breath and remember that you do not have to make a decision right now.
You do not have to decide to leave him forever, or stay with him forever right now. That is a way big decision.
You have to accept however that it is very telling that you feel (and have) like running away. This means things are bad.
I can see you must be confused, as the guy who plays so wonderfully with the children, and who can be so loving to you, also is the person who hurts and upsets you.
A trial separation would be a good idea, as it is not permanent (necessarily) but will give you time to sort out your finances, paperwork and plan for the future.
I think the person to move out, in your situation, should be him. If he refuses, or becomes nasty about it, it only confirms your (and our) worst fears really, doesn't it? Ideally, he should move in with a mate (or hotel) for a week to start with. That is not as "threatening" to him as storming in and demanding divorce.
There are mayor issues of trust and respect.
I would try to be as calm as possible, and meanwhile trying to get a few (financial, logistic etc.) things sorted.
FWIW, my DH and I have had a bad patch, and I have gone through the motions (and emotions) of leaving. Like you I am not from the UK, which made me feel a lot more vulnerable. We sorted it out, but I have to say, we did not have issues with trust (essentially the only reason your H did not sleep with the woman because SHE said no, not him...)or respect. And even without that it was hard enough.
You have my sympathies, and remember, you do not need to make a decision for life right now, you just need to plan the next step. Where to go from here.
Would it not be nice to have him out of the house for a few days? That is a reasonable request and you can take it from there.
Look deep inside yourself for a reserve of strength to deal.with.this.now.
All the best. I know it is hard.