Where would the child be learning this behavior?
Is their domestic violence in the home?!
Have you talked to the parents to find out if its going on at home?
Do they have suggestions for you?
Sibling rivalry starts out at a young age. I wouldn't attribute it to much more than that unless other children are afraid of her too.
Enforcement of the rules, consequences, etc is a good idea. Let her know you mean business right when she gets dropped off. Offer rewards if it helps! OR If its at all possible, keep them separated as much as you can. Split off the room if you can and permit older kids in one area and younger kids in another area. That might help the cause.
I think I would discuss with the parents first and fore most and see what their take on the situation is or what (if anything) they are doing at home.
Personally, it it doesn't get nipped in the bud and NOW, you are going to have a liability on your hands!!!