Things I used to say when my SD said "my mom said..."
"I don't know"
"You'll have to ask your father"
"Sometimes we don't know the whole story"
Above all I never shut her down no matter what she was telling me, I never said a single bad word about her mother (in fact sometimes I almost choked getting out supportive words lol), and I never ever reacted.
Now 7 years later we are able to co parent. Divorce is so hard on kids. It is imperative to keep their best interests in mind. I still remember a particularly rough weekend with her around 7 or 8 years old. I know she has always questioned if mom wants her around, but somehow she got into her head that child support was something dad paid so he didn't have to keep her. This was despite us having her every weekend and being kind and supportive, spending lots of time with her, etc. She lived with that thought for a month (and was a terrible brat lol) before it came out. Poor thing.
Hang in there, you have a tough road ahead of you.