My XW1 very quickly got involved with OM - he moved in with her, brought his kids in, it was a big happy family - She threw him out 6 months later, and was actually very regretful, and changed how she communicated with me.
In my situation I took a very firm stance. I would not give up my time with my kids unless it was just W and them ~ and I would even tell W that. Why would I give up my quality time to allow W to share it with OM?
Once we were D'd, and had things squared away, we are actually very flexible now, and trade all the time. I will say - I stood up to her A and was very firm, but I did it in a very calm flat manner. Never argued, never yelled, never said anything about W to the kids. W carries a lot of respect for me now because of that. Not sure if that matches your situation obviously, but at least my perspective.
