edit; add (since we cross-posted):
That is an important question and one I have already asked. The honest answer (and as I said honesty has been absolutely critical here) is that she would break it off, but very begrudgingly and it would only emphasize the current problems we have.
So she is pretty much holding you hostage emotionally here and putting you in the position of choosing between being the villain who keeps Juliet from Romeo or Cyrano de Bergerac who helps facilitate the romance between the woman he loves and another man. Both stories end tragically.
Where were these problems with your marriage before she fell in love with someone else? By your description, you were perfectly happy and were always supportive of her before, so why wasn't she trying to work things out with you?
I just wanted to add something about dating other women, since other posters (and yourself) have mentioned it as a potential "solution." I understand the general idea behind it, but I disagree that it will solve all or even many of the problems you're experiencing, for the following reasons:
First, I've never encountered a problem in my life that became less complicated by adding more people to it. Every person you bring into your relationship has their own needs, expectations, desires, and personal flaws. The advantage of a monogamous relationship is that only 2 people need to negotiate with one another. Now you're trying to figure out how to incorporate a third person into your life. I don't see how adding a 4th will simplify matters.
Second, I think it's unfair use other people as a "salve" for a bruised ego, a diversion for the problems in your marriage, or to fulfill the emotional and sexual void you are experiencing because your wife has now focused her attachment and her passions for another man. Based on what you've written, you don't want another woman-- you want your wife. You're still deeply in love and deeply attracted to her; therefore, any woman you meet is going to pale in comparison with her. You can't satisfy a craving for steak with popcorn.
Third, generally speaking, unless you're among the top caliber of men in physical appearance who routinely get hit on whenever they're alone in public, it will be much more challenging for you to find a no-strings-attached (NSA) sexual relationship or part-time girlfriend. You will be what the polyamory community refers to as a "unicorn hunter," for reasons that are pretty self-explanatory. You will also be competing with hordes of both married and single men to capture this beautiful mythical creature who is fine with being someone's sidepiece.
Fourth, do you think you're up for dating in a climate that is vastly different than the one you experienced 15+ years ago? Do you have the time, money, and emotional bandwidth to take women out on dates, text and call them regularly, and make accommodations to your life and your schedule to spend time with them both in and out of bed?
Keep in mind that all of these resources (time, money, and emotional bandwith) that you would put into pursuing an extramarital relationship are finite and would thus be taken away (at least in part) from your marriage and your children. Your wife is OK making these sacrifices... but are you?
[This message edited by BluerThanBlue at 3:01 PM, Friday, March 24th]