You need to realise you will get through this, although obviously it will take time
I would suggest ringing the Samaritans anytime you are feeling low, possibly self refer for some CBT too.
Everyone deals with things in different ways, but I probably wouldn't have told the kids anything, the 2 eldest are old enough to work out themselves what happened, and if not yet they would at some point, it's a natural reaction to try to get your point over, but it can cause resentment so I would avoid that if at all possible mate.
Splitting up with someone can be worse than a death in some ways, when someone dies it's final, you say goodbye, knowing there is no tomorrow with them, but a break up, especially when you are in love, people will always think, oh maybe we can sort things out, she's still there, might get back together etc, theres no end as it's always possible it isn't over.
Do whats best for you, I'm not sure you having the kids all the time while she is at his is going to help long term, maybe you should look for your own place and have them over as and when you can, it sounds like she sees you as some kind of unpaid babysitter, you do all the 'normal' stuff, while she's out having fun.
FWIW he would be in a ditch somewhere with his kneecaps done if I was in your position, he knew full well she was married with kids, bang out of order, you have more self restraint than me, which is probably a good thing cos I would probably be in jail if it were me
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Hope it all works out for you mate, but seriously, either self refer for some CBT or make a doctors appointment (who will probably tell you to self refer too) and he might give you some mild anti-depressants (sertraline or similar), as from what you have posted you are quite possibly depressed, even if you don't realise it