Also I have a kid like that in therapy and I found the techniques in the book Siblings without Rivalry to be a big help with brother issues

Aggression can be a symptom of depression in kids. At least in boys.

The worst thing to do for a child with anxiety is to raise them in fear. Don't listen to pps who post just for shock value. She is well behaved in school because she is scared, it is a very classic example. But, your younger child can't be raised in a house where she lives in fear and is abused by her older sister, that is a huge problem. Parents of kids with anxiety are faced with this same issue all the time, lamb at school, lion at home. Patience is needed, evaluation too. To my child, talk therapy made things so much worse, several therapists, all they did was allow the child to talk and put all the blame on everybody else. It didn't work at all, other than as a pity party for my child. I wish it worked but no luck. Find a psychiatrist please.

Beat her ass.

Your younger child will need a therapist too, not the same therapist as the older child.

Please have her evaluated by a reputable child psychiatrist soon. Then you will know more about whether medications are needed based upon the results. You will also need to set stricter limits on her behavior towards her younger sibling. You need to protect the younger one from further harm inflicted by the older one, which unfortunately is easier said than done. I would not leave them alone together until the older one has more control over her emotions at home and will not hurt her sibling with unkind words or physical harm. Good luck to you and your family.

You might have to go with medications. Keep in mind that some therapists discourage clients from talking to a doctor, who can actually prescribe meds. Dont listen to that. Meds make a world of difference for kids with anxiety.

Have you given her the back of your hand yet? I recommend that.