Soaking up this pain to protect your kids from divorce is something you can always be proud of, you'll know inside when you've truly done all you should.
I see your bind. It's clear as glass that she's had/having affairs, but she won't admit it and you want to put something so undeniable on the table so that she can't deny it. You could then escape in some direction from the current situation which has got to be nigh on unbearable for you.
Maybe there is another way to escape from it. I guess at the moment you are acting a bit as if there isn't an affair. How about trying acting as if there is, without actually saying anything about it. How about just pulling right back. Don't see any point in trying to build bridges to her when she is having affairs. Concentrate 100% on doing stuff for you and your kids. You just need to be civil when you see her, like you would be civil with a neighbour, that and no more. Try it for a few weeks see if you get any small changes. Maybe with a bit of time you might feel a bit of respect gradually creep back into your relationship all be it at a very basic 'neighbours' level.
I think problem for a lot of us that have got to this stage of separation is that trust and respect has completely gone, the relationship is destroyed but we hang on to it's ghost because it just takes time to realign yourself to such a massive change in your life. Once you've had the time you need to realign, the ghost melts away and I think you start to see you really have to start from scratch and the foundation is trust and respect. You can't take a step further forward till have that.
