I'm in a triad with a male Dom and female Dom, with me being the sub. They were a couple first. I tend to value independence in my Dominants, but the male Dom is almost 30 and still expects his mom to do his laundry, drive him, shopping, provide housing, cook, etc. There's no disability related reason preventing him from caring for himself, he simply chose to prioritize other things over his independence. He's finally moving out (not by choice) and ranted at both of us about how his mom packed for him as well as other things she "did wrong". This ranting is a pattern and usually sounds entitled and misogynistic.
Both of us got sick of it and separately told him he should stop expecting her to do things. He withheld emotional love from the other female and twisted what I said; as well as denied saying things I have proof in text he said previously. Honestly, after all this, I lost the spark I had for him completely; I don't find him attractive and worry he's being emotionally abusive in private to the other woman. I still care about the woman and am completely lost what to do. Address my concerns he's emotionally abusive with her privately? Break up with both of them? Propose staying with her and cutting him out?
It sounds like you should end this relationship with him, period. You don't want to, and should not, continue dating him. It's up to your other partner whether she wants to continue dating you outside of the triad. You can ask her how she feels about that, and see what her concerns and hopes are.
You should not try and convince or cajole her into breaking up with him. Never give an ultimatum like "break up with him, or I'll break up with you." You can explain your concerns, give examples of his behavior that you find troubling, and be clear about why you no longer want to be in a relationship that includes him. She can then make her own choices.
Obviously, the triad is over, but if you continue dating her, you'll need to be clear with her and with yourself about how comfortable you are with having him as a metamour (partner-of-partner) and how involved you're willing to be in any sex, conversations, hangouts, etc. where he's around. You may also need to draw clear boundaries around discussing him with her, especially in terms of his rants, drama, and manipulative behavior.
It may simply not be possible to make a new relationship work with her, and that's frustrating and disappointing, but it happens. It is absolutely not worth continuing to put up with this guy just to stay with this woman, especially if staying with her means you continue to be emotionally or sexually wrapped up in his nonsense.