Wait wait wait..... I need to break this down, so bare with me because I have some things to point out that will pi$$ you off but help you get through this.
She told you she has been having sex with another man behind your back and when you are ready to behave you can meet this guy???? That you can do what she wants when you're ready to behave on her terms and this is all ok
And yet she doesn't not want you to put any blame on her because somehow she is not at fault???? She wants you to meet this guy who knows she is still married and dissrespects you by daily by sneaking around with your wife while you did everything possible to save your M. It makes my blood boil just thinking about it but I can help!
Do you see that this is an attempt to keep control over you? It is. By having you meet the OM not only is she looking for approval for her affair and cake-eating, she is trying to test you to see if you still want her, are jealous of her OM, and will start a fight so she can jump to any irrational reason to justify her decision. DO NOT under any circumstances put down the OM or try to make her feel guilty about this. Her sense of pride is attached to the OM and any attack on him will be seen as a personal attack towards her and make you the lesser man.
I've been through this situation before and I can tell you exactly how to deal with him, but let me just say DO NOT play her game and meet him! I don't care if he looks like the Brawney man and has money stuck to his skin, there is no excuse for you going out of your way to play her game and meet this guy. You'll have a chance to size him up later and mess with his head (more on that later) but right now you're setting yourself up for a nervous breakdown and bad first impression. And first impressions mean everything when it comes to this guy!
You're wounds are too fresh to handle this, you gotta trust me on this! Give it maybe two to three months.... just keep avoiding meeting him while you take this time to mentally prepare. When you can look at your wife with complete contempt and disgust for her attitude with no emotional hurt left.... you see her every flaw and find excuses not to want to like her, you'll be ready to meet this other guy. Really it may seem like torture and this guy will do little things to assert his dominance (no matter how nice he seems) there's a little Darwinism at play here, but despite all of this he will be jealous of you. Realistically he has about a 1 in 1400 of sticking with her long term since the relationship started with deceipt and will end even faster because it loosely based on just sexual attraction.
There is a chance of him trying to outshine you or passive aggressively bully you in person, but it's easily delt with. Just calmly ignore any pathetic attempts to get you riled up and make it clear that he's trying too hard to impress her around you. You can actually say "hey, chill out... you don't have to impress me in front of her". Sounds odd but it works for every A-hole that tries to tear you down. Or you could go the sleazy route and covertly ask him how your d!ck tastes.... learned that one in the Navy and it completely pi$$es guys off.
What you have to realize is that you're the father of her children and cannot be pushed permanantly out of the picture. You will see her again from time to time unless she moves far far away, which means you have to opportunity to have family moments together for the children.... even one lunch together two times a month will be enough of an excuse. I've read about this approach before and if you can muster up the maturity to see her again on "just friends" dates you'll drive any man in her life off with his own jealousy. I know about this approach with DaisyGirl41. Who do you think told her? It works, but one fight is enough to set you back six months or more.
You have a few options open here with your wife... but I like the one that has you switcing roles as the OM and watching him freak out and get all jealous and possessive. It may take a year or so of very seldom contact, while you're dating other women of course (I'm not going to tell you to hold out undying hope after divorce), but after the sex dies down once they get to the power shifting stage they'll start to have the same fights and arguments over misstrust and jealousy. If you can relax and just sit back you'll really enjoy watching him crash and burn. Seriously, wait for your children to say "where's daddy?" enough times, and for your wife to make excuses to reach out to you because the OM is not so wonderful and treating her like sh!t.
At that point you shouldn't even want her, but hey there is a chance in hell. And if she sheated on you with him, she could cheat with you on him. Just saying the offer will be there for you if you want it within the next 2 years.
Hope this helped. I could go on but I'll save you the long boring read for another time.