Kevin - if ever a D is filed, I dont think it wise to try for full custody. The expenses in such a battle are huge. I believe that since you are already coparenting with a schedule, most any court would try to maintain the status quo for the kids.
After a D, it would be hypocritical to not allow your XW to bring new men into her (and your kids) life. I am sure you would want to eventually date and meet someone new to fall in love with if you were to D. And you would not keep that person secret from your kids.
Introducing kids to the OM hits home with me. My W wanted to introduce the kids to him (who she called "just a friend") and I insisted that she not do it. She agreed. But she went ahead anyway secretly behind my back. I found out about it from my kids. The kids witnessed their mother sucking face with OM. OM even was kissing my daughter. My W crossed a line and there needed to be consequences.
I struck hard and fast (filed for a D with a protective restraining order). I did not show mercy in the beginning. There was always time for that later if she came around but I kept that big gun loaded and cocked. She was pissed at first, but she admited various times that she liked the strength I had. From that point forward, it was up to her to decide whether she valued our marriage and to prove to me that she wanted back. Even though she eventually asked me for another chance, I had moved on. To this day, I dont regret my choice.
My XW married the OM who was "just a friend" a few weeks ago. Things are cool now and we coparent very well.
If ever you do file for a D, you dont use that as a mechanism to coerce your W back. You do it for your own self respect and dignity. You do it because your boundaries have been crossed. You do it because living in limbo has reached a point where you refuse to tolerate anymore. You do it when you realize that you could never fully regain the trust and love for your spouse.