G.T.
You are the mom and you are the boss. You need to take charge and be consistent with punishments until she finally "gets it" that her attitude will not fly anymore the way it is.
Be careful of what she is watching on TV, she could be mimicking some other disrespectful kids she seen.
Lay down the rules and enforce them immediately. Don't take it as a personal attack on you, she is really asking for help and wants and needs the boundaries that you have so far failed at building.
She may need to spend more time in her room "thinking" about how to be nice. Go to the library and get some books for her to read about being a good big sister and other books that have positive messages on behavior. She's learned to be mean somehow and it's making her feel good for some reason.... I say she has something bothering her that you dont know about, and you may need to spend more time just hangin out and talkin to her... take her to lunch (just you and her), she is the oldest daughter and is just trying to FEEL that role. If you start paying a little more attention to her and treating her like the oldest so she feels special, she may not need to bully anymore because her own self esteem will be better.