Is it normal to let younger kids beat up older kids and not step in

my 4 year old beats up my 11 year old and 13 year old twins. she is banned from the playground because she gets so mean with the other kids. She thinks she is a ninja superhero. She also destroys everything and calls everyone a stupid bitch. we adopted her, the shrink can't find anything wrong with her other than she is spoiled. My sons really really hate her and think I am an inaeffective parent. She also beat up 3 babysitters and broke one of the woman's toes and I had to pay for it.I know I should say something because it has gotten out of hand , but isn't some of this the older kids and babysitter's faults for being such pussies. I mean my older kids are all boys and men are supposed to be tough and not afraid of anything .maybe if they didn't live in mortal fear and cry everytime she walks down the hallway she wouldn't beat them up.They should stand up to her and not let her do it. Isn't this apart of growing up and fending for yourself.