You need to lay some ground rules with the kids that this is disrespectful and you will not tolerate it, no more than you would tolerate them criticizing you.
I have done, and continue to do this. One area in particular is the "telling mom what goes on over here" issue. I have told the kids many times, quite clearly, that, unless something is going on at my house that is dangerous, risky, etc., their mother has no business knowing it. They "get it", but continue to tell ex things she has no business knowing. (E.g., that W went to a Buddhist retreat, that me and W were arguing loudly, that W spent money on DD5 but doesn't take them shopping anymore). W tells me that sometimes she feels like she has a house full of "spies" and that she can't relax when they are there. I agree. I lecture. I lay down the law. They follow it for awhile, then they don't. Part of the blame is that their mother is likely cross-examining them.
My point about being a peacemaker was less about soothing ruffled feathers and more about being the "mediator" between the two "camps." Although she may have had issues with me in this regard in the past (that I wasn't advocating her position strongly enough), I don't think that's a big problem today. I was just trying to explain how and why she didn't follow through on "list item" about her being a "loving role model" for the kids.
