Had my wife returned to the marriage, I would have taken her back subject to the conditions below.
1. Never, ever, under any circumstances can she communicate in any way with the other man for the rest of her life.
2a. If the other man reaches out to her, she does not respond and immediately tells me. If he sends her something, she immediately shows it to me. If he tries to contact her via a third party, she immediately tells me. Total openness would be required and that includes email, phones, etc. Yes, even the work ID and email, regardless of company policy. I would have done the same.
2b. If she tries her best to avoid him but he is insistent, we go to court and get a No-Contact Order. We notify the law each and every time he violates it. No warnings. No exceptions.
3. Get counseling. Both of us together. I will take responsbilty for problems I caused. But, she is fully responsible for her affair.
4. Avoid any friends or relatives who aided and abetted the affair. Completely, totally, no exceptions.
5. If the guy shows us at our house, I have a shotgun, a shovel and an alibi, and, I get to use them.
#5 is a joking.
Sadly, for me, and our children, she was too far gone. It would have been work, but I knew guys who had survived and rebuilt the marriage. But that was not to be. Therefore, I took a friend's advice and I adopted the philosophy of "living well is the best revenge".