Hello and Thank You for using Just Answer. I am sorry to hear about the bullying problem with your 11 year old daughter. Children usually bully because they feel inadequate about themselves with regards to some aspect in their lives. They therefore redirect these feelings and take them out on usually younger children. Additionally, it often seems natural for the oldest child to pick on the younger children because they simply know that they have the ability to do so.
Therefore, there are a few things that you can do. First of all. it is a very wise idea that your husband is taking your daughter to the gym. If she is able to shed pounds, she will develop greater self esteem and feel absolutely wonderful about herself and will be able to buy even more cute clothes. For your 11 year old, you may need to create a behavior chart...a daily one. For every time period during the day like morning , afternoon, and evening when she has progressed through each time period without bullying, then she receives a star, happy face, or sticker. If she bullies, she receives nothing but a reminder as to the correct behavior. Make sure she also states what the correct behavior should have been. Then after a she has received 15-20 stars or whatever (you decide the amount), she will receive a special small treat, reward, or outing. The goal is to focus more on the positive behavior and REALLY praise and reward her for it. Also, ignore her tantrums. She just wants attention and do not give into her demands.
On the other hand, you must teach your other daughter, the 9 year old, to speak up when she is bullied. Teach her how to use an "I" message to her sister. When she is bulled, she needs to say (for example), " I do not like it when (you call me names) because it makes me feel (sad) and I want you (to say nicer words to me). Your 9 year old can role play several scenarios with you so she knows exactly what to say. Believe me, it will cause your daughter to stop and think about what she is doing.
Have a great day!!!