First post on this site.. I was about to post a similar story to yours (she has had 4 affairs that I know of, have confronted her on the first two, she reassured me it wouldn't happen again, and I see she's on #4 as I type. Lots of good cuddles to confuse me as to where she is and wants to be in her relationships, etc, but the lies and cheating continue).
I just wanted to chime in and say that ya, as the many good posts above have said, divorce is probably the only option at this point. It's certainly not an *easy* option (especially with kids, and I have 2 as well with her), but less stressful than having to keep tabs on her and wonder what she's up to every minute she's not in plain sight. I haven't told my WW yet that I want to divorce, planning to get my ducks in a row first and meet with an attorney to see how this could play out.
I know you say you still love her. I feel that too with mine, but started asking myself "do I love this woman, or the woman I thought I married?" I believe the woman I married is gone (maybe never truly existed, except in my wishful thoughts?). And think of it this way - no matter how much you love her, if she died today you'd still need to bury her and move on. This is really no different unfortunately. Your wife (as well as mine) is dead to you. No fault of yours. It's unfortunate and outside of anyone's control. I feel your pain.
The thought of divorce to me is like jumping from an accelerating car without brakes. You know you have to jump, and waiting just makes it worse, but still no easy thing to do..
Hang in there man. We're in the same boat and we'll navigate these waters together!