How do I [m] tell ex [f] to stop yelling at my 11 year old?

I'm the father of two easy going girls, including an 11 year old sweet, smiley, nerdy, spacey little kid, and her 8-year old sister. They live with me half the time, and in homes within short walking distance. I'm no angel, but in the rare times I lose my temper, I apologize and explain to her that it's never right to yell, and try to iron out whatever behavior upset me in as mature a way as one can with a tween. I read about an "authoritative & loving" parenting style, and try to model something like that, and I have a great relationship with their kids.Her mother OTOH yells at her frequently, always citing "disrespect." Tonight, my daughter was at her mother's, who purchased some school supplies I already gave the kids. My daughter says, "Good job, mom," and rolls her eyes. In my house this would lead to play fighting and might escalate to tickles.That's when the yelling starts, and sure, I can see how that might warrant a surly response. But in their case there's a predictable pattern. My daughter withdraws, turns her back, or needs time alone. Then her mom sees that as the "real" disrespect, and escalates her yelling and dressing down until my little one is weeping to the point she can't talk.One time, this happened after 10pm when my ex wanted to leave the house for some reason.Another time or series of times, my daughter came home to me with a bruise on her cheek. After probing, she said it was self inflicted "to teach her mom how much it hurts her when she yells." Two therapists I relayed the story don't believe it was self-inflicted. In any case, I asked around and was told very clearly there is nothing legally I can do about it.I hate this. It hurts whenever I hear about it, and it's frequent. They were just on vacation with another family, and it happened in the car in front of everyone.I think my only option is to talk to my ex about it, but when I've asked leading questions, she insists my daughter's behavior is so awful that she feels totally justified to yell. I want to be very careful about the feedback, because I'm afraid my ex will just stop telling me about these fights and isolate my daughter. Are there any resources or advice you can give me that could help me in this situation? via /r/Parenting https://ift.tt/2wQ7SL7