I'm going to try and make this as easy as possible for you, because it does seem like you are doing most of the right things, but that they may need a little tweaking.
Sit both girls down and say, ok, here's the new rules. Everyone has to behave from this point on, or these will be the consequences. I will tell you do something one time, if you don't do it, i will tell you a second time, after the third time telling there will be a time out and you don't get a star for the day (or lose a star they already gained). Ask them if they understand the rules, if they have any questions and then you can even shake hands on it.
Take a simple calender, each day that's a good day they get a star and at the end of the week, they get a prize. Take a shoe box, and fill it with dollar store items.
Punishment should consist of time out. If she will not stay in her room for the time out, then fine, take a chair, put it in a corner, or a hallway and her time out is sitting in the chair. If she gets out of the chair, pick her up and put her back in the chair, even if you have to do this 100 times. Even if she is kicking and screaming, you tell her she has to stay in the chair for her time out.
If she goes for more than two days completely not listening. Consider taking items she really likes, even if it means taking a ton of stuff out of her room. Let her know if she can't listen then she cannot have extra privileges.
Be sure to take out at least 15 minutes, twice a day, to sit down and talk to her about how she's feeling and how her day is going and if there's anything she wants to talk to you about.
Praise the good. Let her know when she has behaved well. Ask her sister to praise her when she does well. Praise her sister when she behaves well, especially in front of the 4 year old, but do not direct the comments to the 4 year old (look how good your sister is behaving) instead, just speak to the sister (thank you for behaving so well, or thank you for taking the plates to the trash, I really appreciate that) and don't even look at the four year old. She will desire to have that same praise.
Whatever you do, you have to stick to your guns, be persistent and be patient. She didn't get this way overnight and she will not change overnight. I welcome your thoughts, let me know if you want to talk more.