To me it sounds like introducing kids to ANYONE is a step that should be weighed. But maybe have these conversations ONLY during the counseling session. The MC will masterfully (if he or she is skilled) use words that will avoid the traps and pitfalls that make us fight.
I have a colleague here who cheated on his W but they have a S together and they have a very amicable R. His W. was THRILLED when he started befriending me and my W. She thought it offers stability to the S. and a good influence. Very funny that of course my W and I pretty much around that same time started our own sitch.
But I think regardless of where you and your W are and what the end result is, the two of you SHOULD work together in deciding everything around the kids. I don't have kids but to me that is a boundary that has to be respected. For the kids' sake in fact. They need consistency.
