Hi! I believe I can be of help with this issue.
First, let me say I can imagine how distressing this situation must be for you. On the one hand your marriage is a wonderful marriage. But on the other hand your wife has broken your trust for the second time now.
And this is actually the key to my answer to you that you need to consider and think about. This is very unusual that your marriage is THAT good and yet your wife feels this compulsion to have affairs. It points to perhaps some childhood trauma for your wife. But even with that, usually the marriage has other problems and is not so stable and satisfying. Perhaps the marriage is not as satisfying for her as for you. Yet you report that she terminated couples therapy after 2 years. Again, 2 years is a long time to be in therapy if she didn't feel it helped. So, this is all very unusual.
Another unusual part of this story is that the driving force for you to get a divorce seems to be your kids, not you. You give the impression that if your kids were not involved, you would stay in the marriage. Yet you write that you want to stay for THEIR sake. I can't imagine they thought you should leave just starting now with THIS revelation.
So, what we have here is a marriage you are satisfied with that includes periodic affairs on your wife's part. I don't think you should let your children rule your decision. To leave because they would lose respect for you if you stayed seems like a bad trade off on your part: You may be thinking about living the rest of your life alone and have decided you don't want that.
Therefore, I would like you to really consider whether you want to leave for your OWN reasons and if not, explain to your kids how much you love them and that you understand their point of view and value it but that you have made your decision based on your needs. That you know full well what you are getting by staying with their mom but that this is what is important to you. It will then be up to them to adjust.
You may seek couples therapy with her again. If so, consider the following types of therapy. One type of therapy is called Gottman therapy. Seek a therapist who is certified by the Gottman Institute. Here's their web address for finding a therapist:
Why? Because John Gottman is the foremost researcher in marriage today and his couples therapy model is the most straightforward model available.
The other therapy is Emotionally Focused Couples Therapy. This one is the one I would use in your situation perhaps even before Gottman. Why? Because it focuses on how there have been created emotional barriers and how to get through those barriers. I imagine your wife might need this aspect of therapy. Please consider it before you take other action. Here is the web address for their therapist finder:
On the website you'll also find excellent books by the founders, Sue Johnson and Leslie Greenberg.
Okay, I wish you the very best in this and in the future!
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