User blog comment:Zathronas/Analysis by an author: Volume 2 episode 6: Burning the Candle/@comment-10390252-20140905091829

FWIW, I suspect that Cinder may be Yang's aunt, her mother's very much younger sister.

Anyway, my reading of Yang's flashback is that she was running away.

Her father's breakdown after Summer's death was so total that he couldn't care for the girls anymore. After learning about her biological mother, Yang became obsessed with finding her in the hope that she would be able to care for her and her sister. That is why she brought Ruby with her, by the way. She was hoping that she was taking her sister to someone who could care for her. No five-year-old should have to make those sort of decisions.

I have do doubt that their father shaped up after that. Mostly because I think Qrow would have beaten him to a pulp in a way Yang wouldn't notice and told him that he would have warned that he would finish the job if there was even a hint about him neglecting the girls again.