Dear M.,
I would say that you are right, she is definitely jealous, and she is in the stage of development - 6 years old - where she is practicing being what shall we say - a very bossy woman. Six year old girls are famous for bossiness.
They need to watch the 3 year old carefully to keep him safe, it sounds like the attacks are getting scary.
AND, they need to spend a lot of time working with the 6 year old little lady. She needs to be taught , very carefully, taught what her role in life is. For one thing, she is a big sister - Protector Role, she is a little girl - NEEDS Love and firmness - she is GOING TO BE A WOMAN. Her mother needs to come right out and tell her and guide her about being a woman that is caring.
I told my grandson recently that if he wants to have a relationship with another girl friend that he needs to chose carefully. Our family is tired of having to endure the uncaring, lazy (yes, sorry) , demanding behavior that seems to be rampant these days - in the age group of 18 to 50 - quite a large span, I know. I have been paying attention and that is the truth. If the girls in that age group are mean, they are very 'mean and selfish', if they are caring, they are very very caring. Time for caring to come forth to conquer 'mean and selfish' .....and it begins right now at 6 years old. Yes, it does.
Your friend may not like this , so you should blame me for the whole thing. But, we can say that we warned her. Mothers are the very first target of the meanness behavior. Umhuh, that is right. (except, of course, unless a little brother is conveniently in the family).
Punishment does not work, it just makes it worse, guidance and training and helping her to care about other people.
Sincerely, C. N.