You keep saying this is all about protecting your children. Protect them from what? Do you think your W's boyfriend will beat/sexually abuse, shove booze & drugs down their throat or what? If you don't have hard evidence that your W's boyfriend would do such a thing then their is NOTHING to protect them from. People get divorced, they move on and date. It is how life sometimes works out. IMO it seems your strong desire to "protect" your children stems from a fundamental difference you have with your W (you not wanting OM around, your W wanting OM around).
And, I don't know quite how to say this so I simply will be direct. You are *so* worried about protecting your kids from OM but you didn't seem to have a problem contributing to their confusion when you and your W play "happy family" on holidays and b-days so both of you can save face and indulge a fantasy for your children that most probably will not come true (mommy and daddy being together). To me that is FAR more damaging than your W and OM taking the kids bowling.
You are certainly welcome to have any belief system you want but you can't demand others adhere to that belief system in the name of "protecting" your kids.
You have asked your W NOT to involve OM with the children and she decided to go ahead and do it anyway. There is nothing more you can do about it except realize this is just another HUGE sign that there is NO marriage to "win back" or "rebuild".
You smothered your W and now you are smothering your children. Once the D proceedings are over you will be single man and your W will be a single woman and there will come a time when you both have intimate R's your children will be exposed to.
I was so pleased with you last week but now it seems you are falling back to your old ways.
Tell us what you are protecting your children from other than a very different belief system than your W has?