As you know you are on a terribly slippery slope. I would say that your responsibilities -- morally, financially, and common-sensically are to your wife and children.
Work on Marital Problems with Your Wife
Now, if there are problems in your marriage, you should be working on it with your wife. Seeking refuge outside your marriage may sound attractive, but is it worth the consequences? You seem to have the same question, but the answer can only come from you.
Are you willing to work hard to save your current life? Can you get some support from someone besides your new "friend?" I mean, can you talk about this with people who don't have a vested interest: church leader, therapist, a coworker?
Your Judgement is Impaired
In this situation you are like the drunk driver with the keys in his hand. Can you handle the car? There is no question that your judgment is impaired at this point. Can you find a designated driver until you sober up?
In this situation, don't act hastily...take it slow...if it's meant to break up, establish that, but don't leap before you look. Of course, you probably won't take my advice, but let me know if you do!