If you can't provide a wholesome, healthy environment for the kids in your current situation then you need either get your wife working with you to change it (in other words, she works on the marriage) or get her out and get a loving female role model in for the kids. Your wife's current mercenary attitude needs to change or she needs to be shown the door. That's my opinion. Since you've researched the alternatives you need to make that fork in the road decision. Talk directly to your wife. Let her know that you're aware of her most likely having an affair and that it probably started over 3 years ago before things went to pot in the marriage. That it may be another man than the original, but it's rare for a woman to act like her and not be having one. Let her know you're willing to work on the marriage, but only if she is. Also, since you suspect her of having an affair you need to stipulate that she gets a clean bill of health before even THINKING about inviting you to bed in the future. You don't need to risk your life for her and if she balks at it then it's a deal breaker in my book. Your kids need a father, not a walking STI.
Sounds harsh, but you've been dealing with this for years and it's time to make a choice. Check out Chocolateyes thread, he's having a simliar experience with his wife and it might give you more insight.