My friend, I've gone through nearly the same experience. Married 10 yrs, had the picture perfect life, then my wife ends up starting a "close friendship" with a mutual friend of ours. Exact same behavior, she wants more alone time to go out with friends, she doesn't want me around to things we normally did together, she didn't care if I slept with other women (which I had ZERO desire to do), she was Myspacing this guy and searching for him "just to check up", they were "just talking" and being friends, she deserved to have whatever friends she wanted, etc. I required that they never speak, which she complied with for a couple months, but just went right back to him after. Seeing your words below made me relive the emotions I felt back then, and it was identical to you. It's truly a nightmare to live through.
What she is doing with this other man is connecting. She is sharing hopes, dreams, problems, laughing...all things she should be doing with you. You are 100% right to believe that a married woman with 4 children should not be going out to bars alone, and suddenly having boy friends. Unfortunately, it sounds like she has checked out mentally, and emotionally from your relationship. You can read as many books as you want to, and I do recommend you do, but it takes both sides working and wanting the relationship to succeed. The more you push to influence her, the more she is going to back away.
When my wife was doing this I did confront her about it, but she always claimed it was nothing and that I was over reacting. I knew in my heart I was right, and had I to do it over again the only thing I would have changed is this: I would have sat her down and explained that I knew what was going on, or what was about to happen. And that if she continued her behavior that I was going to move out. I would have rather been in control than at her mercy, which was the position I had put myself in. That's just what I would have done, your situation is unique to you so that's not necessarily a recommendation.
I truly hope you can work it out. I'm a huge believer in marriage and family, and it breaks my heart to see any family torn apart by this reprehensible behavior. But having lived through it myself, I would start to put a lot of thought into what you're going to do in the event this marriage fails.
Fortunately, while I would have never desired a divorce, life after marriage has been awesome. I too was terrified initially, but if you treat it as an opportunity rather than a set back, you'll be pleasantly surprised.
HTH...