Alan, I think you are doing this thing as "right" as it can be done. That is small consolation, and I can definitely sense the pain you're experiencing. But I also sense something else: That pain, strong as it is, is not as strong as your mature, "try to take it like a man" fortitude and reasoning which will serve you, her, and the kids well through this time.
It also makes me think there really might be a chance she eventually realizes what she had. Few men have that kind of fortitude and strength. She will come to understand and appreciate that eventually whether she comes back or not.
And whether you take her back or not. I know you don't believe this right now, but it may be that you do not want to take her back. Maybe I'm a hopeless romantic at heart, but I know for a fact it can happen. It happened to me and I didn't think I was very strong at all.
I had to leave the area completely and start a new life when she left me. A clean slate and all that. New conquests. Old friends. And for the first time in years, everything I did was for
me! I started to really enjoy life again. Hunting, fishing, beer drinkin' with my buddies, womanizing and shamelessly carving notches in my gunbelt. Truly Free and single is not an entirely bad thing once you remember how! It was actually easier, being "experienced" and therefore, far more cynical, than when I was young and "overly eager", too.
Then one day, a familiar knock on my door... She had FOUND me!

And there has been no escape ever since!! :{ :-laf I am DOOMED to having to hustle and seduce the same woman over and over and over again for the rest of my life!!
IT'S GROUNDHOG DAY!!! And for the same thing I've already had over and over and over again?!! We men really
are idiots being led around by our jonnies like that. Not that
I could ever be p-whipped or anything, of course...
Honestly, she was almost too late and she will never know just how close it was. I had been seeing a woman I once knew from a long time ago and things were on the brink of getting pretty serious. I had a very tough decision to make...
I have never kidded myself about being as smart as Einstein. Nobody is. Even he, the Father of the Theory of Relativity and countless more unequaled feats of reasoning out the
Secrets of the Universe, could not figure even
one female out, and ended up divorced... :-{}
Don't beat yourself up. Play it cool and maintain your self respect. You owe that to yourself and kids. And that's all you owe anybody.