Have you asked (since you are the newer person) if the jealousy is not about sharing HIM, but sharing YOU?
That he gets more time with the newer person than she does?
My introduction into the mix has created the need for some additional pieces of communication between them - particularly having to do with time. She was feeling somewhat dismissed and acted out.
What does she need for better communication or time management? From him? From you? Did she articulate what her needs are? Or only express her emotions at this time?
I still have an underlying issue. Chiefly, that although they both state that they don't "do hierarchical poly", in reality, that's more or less what they have. I still feel as though I need to get approval from her to spend time with him.
Did you ask what behavior is expected of you? "Do you expect me to get approval from (her) to spend time with (him)?"
Then once you know what is expected you could
- agree to do it
- NOT agree to do it and that's it
- NOT agree to do it "that way", but offer to do something "this way" to see if the need is met with another method