LW, keep sending cards, and do your best to keep sending cards after she moves out, too, if you can do it without being creepy about it. I had a cousin in this situation (and no, we don't know why my uncle was cut off, neither he nor my cousin ever talked about it to the wider family) but her aunts and uncles made the effort to at least send Christmas cards and the family reunion invite when they had an address. It meant that when my cousin's mother also lost contact with her and she was in a really bad situation, she knew she still had people she could contact for help who still cared. (And it wasn't a "Mom is the villain" situation even then - Mom was in a really bad place too.)

She's never been as close as the rest of the family and never really worked things out with her dad, though they eventually spoke sometimes and she was able to be POA when he was very sick; don't expect it to be the way it was and definitely don't pressure her for that. But yes, unless she contacts you to ask you to stop, keep the door open to her, of course!