From what you are writing, it seems that T and K have a very unbalanced relationship, with K calling all the shots and T left unhappy. Are they into poly relationships, or is the open relationship model about sex only and not emotional attachment? Perhaps the emotions T feels for you are the big threat here. Also, Ts former cheating (how has she "cheated" in an open relationship?) may still be having repercussions of mistrust for K.
This really doesn't sound like an issue you can have much say in. If your partner is alright with this and you and T know your feelings, it is in Ts hands. She has to decide what it is she wants-you or K or both-and work towards that. By expressing your feelings, being honest, staying within the boundaries they set so far, and talking to K even after the abuses, you have done pretty much all you can. The remaining issues are theirs to face. All you can do is step back as far as you're comfortable and hope they work it out. I wouldn't stop a friendship based on a jealous gf if I could help it, but wouldn't push the boundaries of that friendship either. Not while the negative effects are still so intense.
I'd rather be hated for who I am than loved for who I am not.