I think you're trying too hard to influence DD's relationship with her mother. It might be healthier for you to back away a bit. The coaching session you offered her sounds counter-productive to me. It just amped up the level of drama. Your daughter is seeing a counselor. Let the counselor do the counseling.

Naturally a father is also a counselor to a daughter, but this is an issue you should handle with a very light touch. Your ex is trying to buy your daughter's allegiance. DD may be tempted to take the bait. That's up to her to figure out for herself. Your ex is also out to make you look bad in your daughter's eyes. That's not going to change. You don't need to get defensive. Your daughter lives with you and knows who you are.

DD and her mother have to work out their relationship in their own way. Don't be in the middle of that. Your daughter has been exposed to excess drama related to this divorce. Kids can get addicted to drama and find ways to keep it going. Try not to feed in. DD and her brother will also work out what's between them in their own way. Your daughter will have some inner conflict about how to relate to her mother. Having inner conflict is part of life. It doesn't mean that all is chaos. Resist the temptation to do your daughter's thinking for her. She'll have ups and downs with her mother. Just give her a stable base in a stable home, and she'll figure out what's what.

Your ex bringing a guy with her was not very classy. So . . . she continues to show who she is.