T.M.
I would not have contacted the child. If it was my child i would not appreciate another parent reprimanding her. That is my job. I am by no means attacking you.
Have you thought about it from another perspective? Having her over gives you a chance to see her true behavior. It also lets the child see how another family acts. (in a positive manner)
I do understand where you are coming from. My 10 year old has a bossy friend. I cringe when she comes over. I do politely remind them all to be nice when they are playing. (i direct it to all of them, hoping that she gets the point)
11 is a tough age. They are pushing their boundaries. They want to be teens. I have 4 daughters and am one of 5 girls. It is all normal. They need to be gently reminded. But, not on fb and not directly to the little girl. That is not fair to her.