You describe your wife as passive-aggressive, combining the silent treatment with expressions of disgust and lashing out. You also mentioned that you have been through two rounds of counseling already with little to no effect. On the other hand, you worry what growing up in such an atmosphere will do to your children, and it sounds justified.
From what you have been writing for a good two years, your marriage is over. Whether you or your wife will change the legal status or continue to work on agreements in any form is not our business, but as far as the personal relationship is concerned, it’s probably over. If you consider counseling, it should not be marriage counseling to make your marriage work (you already tried it), but how to accept that, maybe work out how to fully split or whatever agreement you need to move oon and get over it, for you and your benefit.
Your daughter needs help. It seems she’s not only influenced by her mother’s manipulation (low self-esteem, refusing contact with you, probably to placate her mother), but adopting the same behavior patterns or at least exploring it in a play context. The latter is for me a red flag. Please consider finding a therapist that helps her - as a parent, your intentions are good, but you are a part of the whole situation, no matter how objectivelyobjective you are trying to be. A therapist can also discuss how you as her father can help, maybe in ways you are not seeing yet. You may have to consider that she “lost” you four years ago when the separation started due to work issues.
You could continue asking this community for advice on specific instances or observations. And we will certainly chime in with our thoughts and suggestions. But this is a bit like putting a few bandaids on a wound that needs proper cleaning, maybe a little surgery and stitches. We can provide bandaids, but for a long-term solution in your case, I can only encourage you to find professional help at your location. I am not trying to send you away, but actually help. If you want to talk, remember that all Stack Exchange sites have a chat, ours is The Playground. Take good care of yourself, your kids need you, even if they are pushing you away.