Re: World has been turned upside down in a day.
Working on a marriage, even with marriage counseling, is pointless when one person is actively tearing it down by having a relationship with someone else. If your wife sees that she can pursue her affair partner while you are working on being a great husband and waiting for her, she will only continue in her affair and the marriage will continue to deteriorate. The marriage will never get better or heal while she has another man involved. He is literally between you.
I would recommend that you inform his wife immediately. That will help shut things down quickly. It is highly unlikely that he will continue on with your wife if his wife knows what's going on.
Begging her will make you look pathetic and weak. I'm really sorry, but that's the truth. She will see you as less than she already does if you do that. She'll also see that she's holding all the cards, which you don't want at all. Right now, she is the one who should be begging and pleading with you - willing to do anything you ask of her to resolve this.
One thing to keep in mind is that the woman you thought you could trust is not trustworthy. You will never be able to trust her again unless she gets to the bottom of what would allow her to violate basic moral principles and betray you. If she can't find that and correct it, she'll do it again.
Bottom line is that she makes a choice now - either stop all contact and work on resolving whatever has caused her to betray you or leave.