I don't think this is a "mean" kid, I really think its an emotional or psychological issue.

There needs to be another adult in that room, especially in this case. That little boy needs more attention, not annoyance (Not that its your sisters fault, she's wonderful for taking care of those kids. I'd hate to get bit and hit too!) - this sounds like a special needs case.

Is there anything that the school offers special needs kids?? A private school should be able to afford anther teacher/caregiver and some help for this child and his parents.