My Poor Baby Doesn't Want to See Her Dad but Bare Minimal

Sounds like she will "break his heart" either way, whether she testifies for less visitation or just skips it. She needs to talk to him or write him a letter while she is at his house (so it doesn't look like you put her up to it). She can leave the room when he is fighting with his wife. It's hard to leave when he is criticizing or cussing someone out behind their back, but if she has the gumption, that might give the message more. It's not working with you intervening even though I complete understand why you are. He's taking it as criticism and it sounds like it is making him cling to his position even more tenaciously.

I don't know if they will order supervised visitation just because he fights with his wife. I think your daughter is going to have to tell someone - counselor or social services - that she doesn't want to go under those conditions. Maybe just have some dad/daughter time outside of that environment???

By "all she could do not to cry" I hope you don't mean with the counselor -- she should definitely let her hair down there! Perhaps her Dad will go to a counseling session at the counselor's request, and leave you out of it?? Maybe he needs to hear it from an objective source?

Unfortunately kids dont get to pick their family.
Giving her coping skills is the best you can do for now.
The world is full of disappointing, annoying situations.
Tell her to curl up and read a book and just block her dad and smom
out when they decide they want to bicker with one another. It has nothing
to do with her, she needs to learn to ignore and embrace the good parts of the visit.
Some couples argue all the time, that's their communication style. Neither she nor you can tell your ex and his wife how to get along with each other now can ya?
Her deveolped fantasy of dad divorcing step mom and she having him all to herself is probably not a healthy fantasy to feed. I'd work more on teaching her to deal with their "style" and when she gets older and little wiser I'm sure she will be able to verbalize to her dad in a way that may help eliminate the problem.
Broken homes come with a lot of chrapnel.

I think you need to explain to your daughter that Daddy has problems, the problems are not related to her, that it is sad she has to witness these problems, most grown ups would not fight like that in front of children , but again, her Daddy has problems(like a sickness) that cause him to make bad choices. You'll need to say this over and over. Just be matter of fact like you are explaining a gambling addiction, alcoholism, or mental illness. It is what it is. and it is sad she has to see it but she needs to know it is NOT normal. it is not anyone's fault. Try not to sound angry at Daddy (although I would be) just feeling sorry for him because he has a problem. then she will feel she can talk to you about it without making you very upset or angry. It is so important she feel she can continue to tell you EVERYTHING sand that is why you need to be very calm when discussing it. The counselor should be able to tell you how to talk to her, better than I can. Good luck!

She needs to tell her dad how she feels. (I have an almost 8 yo and they are capable at that age.) YOU need to let her practice wording, help empower herself to express her feelings to her father. Otherwise, say out of it. This is perhaps O. reason why God hates divorce. No O. thinks about this kind of thing down the road and the kids really suffer. She will suffer less if she can express herself in an open, honest, non-confrontational way.