You do probably need to let your L know about the kids being around OM. I am not sure what state you are in so I dont know if adultery applies, but regardless, showing promiscuous behavior in front of children is not going to sit well in divorce proceedings.
Very sadly the law does not protect the kids from this and its even socially and morally accepted in the so called "advanced" societies. We live in degenerate times. Just look at all the stories here. My W went on a cruise with the kids and OM and stayed in hotel rooms where she slept with OM in the presence of the kids. Apparently the D filing is license to do all this. In this system all we can do is check OURSELVES from this sort of behavior. Kerry's W is living with OM (Ed) and there's not a damn thing he can do about it other than go to the batting cage and hit a come run imagining Ed is the ball.