Granny Rose is a member of Cash's group, the "Singin' Strays", and seems to be the most distressed out of the entire band at Copper's banishment from the group. This leads to the entire band's sadness, and eventually each of them end up parting ways, due to the chaos and tension.
Eventually, though, at the end of the movie, the band makes amends and forgives everything that has happened. Granny Rose, along with all the others, sings one last song.