Anyway what MY thought on meeting OM was, was this. IF she intends to introduce him as her new man and someone that my kids will live with, then it would be a good idea to meet him. Though as mentioned that is for the future.
I haven't read the other's responses, so I may repeat what they've already said. Although most people could empathize with a parent feeling anxious about new adults being introduced into their children's lives (via the wayward spouse), the cold hard truth of the matter is there is very little you can do about it. She has the freedom to bring her friends and lovers around her children. I don't know if it is a law everywhere, but in my state, it is unlawful for two unmarried adults to fornicate under the same roof where there are minors. Frankly, I don't see this law being enforced in this day & time, but I suppose the LBS could use it for grounds to have sole custody, IDK. Still, she'd have visitation rights, and how could you control who meets your children while with her?
What I'm saying is that without some type of legal action or something written in the divorce decree, I don't think there is much you can actually do to control who your WW introduces to the children. I know of one case where the divorce decree or custody papers stated that if the mother brought a man to stay in the home (for obvious reasons), the father would have full physical custody of the children until they were 18. And, funny enough, that's just what happened!
My question to you is, how do you envision meeting OM? Do you plan to ask him questions, in order to evaluate whether or not he is fit to be around your kids? Do you not think he would be instantly defensive, maybe making things worse (depending on the depravity of the individual)? What happens after you meet him? Talk to your WW about how it makes you feel?
Before you jump, I suggest you research your state laws regarding this subject.
(((hugs)))
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!