11 years old is much too young to be home alone all day, much less with a younger sibling. Even 13 years old is pushing it. Alone, maybe. With a younger sibling, absolutely not.
If it were me, I would call Child Protective Services. You might wait a couple of weeks after the incident you mentioned so it won't be totally obvious that you are the one who called. But this is a bad situation and it is not going to get any better unless someone does something about it.
Good luck! |