I think that's a great idea, Barbara. Appeal to the marriage's history, and say something like:
"I think we will BOTH regret it if we allow our marriage to end this way. Our kids are at VERY formative years for how to deal with relationships, and relationship conflicts. Is this what we want to teach them -- to cut and run when things get tough? When mushy, romantic feelings disappear? I still love you, despite the foolish choices I feel you've been making recently. I don't want a divorce. I'm asking you to commit just 6 months of your life to really trying to deal with our issues, WITHOUT a third person involved, and then you're free to do whatever it is you want to do. I also think we need a good marriage counselor to help us do that, but we can't do it when you're actively in an affair. Will you consider ending it, and coming back and working together on our marriage? I promise you I will give it our best effort, and we can then BOTH look the kids in the eyes and tell them we did our best."