I don't see how her reaching out to you is experienced as a rejection by you? It's just taking her a really long time to actually do the reaching out. You say you don't know why she turned away from the family; be curious and anxious to talk with her instead of thinking of each of her calls as a single entity and thus a rejection when she does not follow through yet. If you do not feel she or the family did anything "wrong" then there is no reason not to "trust" her. Eventually you two might/might not get together. If you miss her, tell her the next time she calls. If you are on pins and needles because of the constant approach/avoidance dance she appears to be doing, tell her that's how you feel; that you are anxious to get together with her and this to/fro thing is "killing" you with anticipation.

I would look at my own life and why I am responding to my sister the way you are? Did one/either/both of your parents do a similar thing to you; promise you things and then not follow through? Your sister is just your sister, "even" with you, not someone who should have that much power in your life to cause you that much hurt.