I personally believe that it depends on the maturity of the child. My oldest son is 15 and I just started letting him stay by himself last year and that was ONLY if my grandparents or aunt was home. (We live next to them.) I still won't let him babysit my youngest son that is 5 alone. I may when he turns 16 but not before.
I used to be a 9-1-1 operator and you would be shocked at how 7, 8 and 9 year olds not only stay home alone but also watch their younger siblings!
I don't know if my comment helped you, but I would offer this advice. If you are concerned about her being alone, help mom make arrangements with a neighbor or offer to come by and help out when you can.
Good luck and by the way, you sound like a FANTASTIC sister to be so concerned!! God bless...