My friend does this to me too... I'll often be in the middle of something... chasing around screaming kids or whatever, late and trying to run out the door, and she'll call and unload and start chatting... not even once asking if it's a good time for me to talk, or what I'm up to.
I am like your sister, ho-humming on the other side of the phone and 10 minutes in, I finally have to interrupt and say, "I can't talk right now". It's that, plus I just don't like talking on the phone.
Maybe, had you asked if it was a good time for her before starting to talk, or asked if she had a few minutes to chat, and ask how she's doing first, it would have helped with that.
It does sound like she's disconnected from you all though. I don't know if you all text or facebook at all, but those things have helped me to reunite with my less active of family members. I'll just send them a quick note once or twice a week and eventually they start replying back, and we actually start to chat and get to know each other after a while. Maybe that can work for you all.
Also, since you all live kind of far, maybe you can arrange to meet each other at a local park or play area on the weekends somewhere in the middle of your cities.
She may be uninterested and snotty, but don't write her off, she's your family and families always go through ups and downs. You all may be closer one day, it just takes time for some people. Every person has their differences that we all have to learn to get along.