Rushes Bear is Nector's mother and Marie's mother-in-law. She had two husbands: Nanapush (i.e., Lulu's uncle) and Kashpaw. She seems to be a force to be reckoned with—even Marie, who is tough as nails, is afraid of her (by her own admission!):
Although I'd faced down the raging nun and had no fear of my own relatives, although I wasn't afraid of the French priest, although I had slapped away men who came to work on Nector when he was sober, I was edgy in the presence of Rushes Bear. (5.2.5)
Of course, you probably aren't really surprised to hear all this, given her name. No joke—according to family lore, she did actually stare down and charge a bear. In learning how to deal with her mother-in-law, Marie definitely kept that story in mind:
Nector's mother got her name from the time she went at a bear, no weapon in her hand. As I have heard it told, the bear turned from her straight charge. The same with me. I learned not to meet Rushes Bear head-on. (5.2.1)
After a rocky start, Rushes Bear and Marie ended up having a great relationship, with Rushes Bear really softening toward her daughter-in-law when she sees how tough she was (and how much they had in common, as two lonely women). So, at the end of the day, she showed a bit of a softer side that you wouldn't necessarily expect from a bear-rushing mama.