There is, without doubt, significant jealously on Caitie's part. You are the other woman to her, quite literally.
It is somewhat natural for her to feel some competitive feelings with you. But, the pain she has, the utter aloneness and hurt that she feels, (which you did not cause) is pushing these normal feelings of hers into overdrive. She interferes with your relationship with Tony because she wants to make others (you in particular) feel as she does; alone and in pain.
As you are a woman, it is easy for her to dump her feelings onto you. You are the "bad one" in her mind. Not really of course, but her transfered feelings can be very powerful as you have seen.
Complicating this: Her father has really bought into the feelings that often accompany a divorce or remarriage. He is struggling a great deal. He has marked and obvious boundary issues with Caitie, and feels he must try to keep up the "love" or he fails her in some way. (Better said, he fails himself when he feels he does not)
So, he too must grasp the dysfunction of what he is doing so that he can place boundaries on what he is doing/allowing with his daughter. I feel he is trying to be her friend, not her father. That is where a critical error is occurring in my opinion. He cannot be both at this point in her life. Later, yes...but not now.
To recover from this, she must respect; then love him. It is not easy to create that balance, but do so, he must. He will not be liked in the process, but he has to accept that.
You mentioned your own guilt. That too is understandable. Each day you are treated by this young woman as an intruder, an interloper. How else could you feel? You love them both. That is easy to see. But, the feelings you have, although normal, are not founded in reality. You didn't take anyone away from anyone. You are an adult, and you and Toni have something that far exceeds Caitie's teenage anxieties.
But, know this: You are not wrong here, just placed into an incompatible role. Encourage Tony to stand up in a loving way to his daughter. Refuse to be anything but who you are, his wife. And know that with the help they are getting, this can pass. Hang in there and feel free to ask for me again if you need to talk. Steven