I know how you feel. If he chooses to let her watch them there is really nothing that can be done though. She is old enough now to be able to say "I don't want to watch this daddy, can I go play instead". She is 6 not 3 or 4 anymore.
She can let him know her choices. If he is wanting to watch something with her then she needs to verbalize to him that she wants to watch something appropriate.
If he chooses to not listen then she can talk to her counselor about it and then next time you guys go to court the counselor can be called to testify about him not listening to her. That will carry weight in the court room and the judge may make a ruling that shows not rated for her age group should not be on for her to see.
Now that does not mean he can't watch it himself when she is there, it means if she is sitting in the room he would need to turn it to something else. If he wants to watch it she would need to go play in a different room.
My grandkids love to watch the CSI shows, Castle, NCIS, all kinds of shows like that. I don't care too much. My grandson's all time favorite movie is Ghostrider. I caught him, in the middle of the night, watching it on the TV. He would beg to watch it again and again. He was 4.