I haven't read all your back story, but just based on your summary above, I empathize. I have had a similar sitch with my XW....even today, she still sees OM one day, and tells me she wants to be with me the next.
I have told her in the past, I will not have a relationship with her (outside of co-parenting) as long as she has a relationship with him....regardless as to that is friends, or something different. Her solution has been to lie and hide it, so that she can cake eat (make no mistake...that is what your H is doing too).
The only reasoning I can come up with for this behavior is that I was fulfilling some of her needs and OM was fulfilling others....and as dysfunctional as that seems, apparently it's an attractive solution for her. As weird as I find the sitch, it sounds like you are in a similar boat.
So let's fast forward a bit. I actually sat my kids down this week and told them (the teens anyway), that I would no longer be treating their mother like she was a friend (I would say that is a reasonable description of our relationship for the last 6-8 months). I still care for her, and I am not going to be mean to her, but it's simply not healthy for me to be around her or be friendly with her given her behavior.
As I asked my kids...if you had a friend that lied to you all the time, would you want to hang out with them and be friendly? Pretty easy answer. You have to do what is best for you.
