Jumping in here for a bit but if I stay too long I get upset all over again - we have one of those situations that is the epitome of a bad divorce.
We have struggled because the ex told dsd that DH walked out on them (he left when she refused to quit her affair), that he was going to hell because he is Jewish, and that I messed up their relationship (I met DH after the ex married the guy she had the affair with). We'd love to rat the mom out but dsd is 10 and has started doing the math and realises her stepdad has been around longer than DH and the ex have been divorced. Besides, no matter what, I believe that a child have a sound relationship with their parent and that is more important than anything.
I will say that the things that her mother said for years had serious consequences regarding my relationship with dsd, dh and dh and dsd. We tried to say nothing and just correct the lies but she is with her mother more and what child wants to believe their parent is lying to them.
Now whenever the ex is mad she withholds visitation and stops dsd from talking to her dad. It's really hard on the other 3 because they miss her and want to know when they are going to see her.
Compound it all with the fact that our parenting styles/lving choices could not be any more different and it's just a mess