S.F.
Well... this isn't a fix, but maybe a different approach. I believe behavior is related to establishing a sense of security, confidence and position in life. Our behavior becomes poor when we are frustrated, do not feel appreciated or loved or we do not know a better way.
Some of her response may be dominance. We all test our boundaries in different ways and at different times. Those moments may be fueled and poorly handled because of feelings. Some acting out may result from trying to gain attention and specific responses from you. She wants to show affection and gain affection, but she doesn't know how to. Tell her that if she wants to be around you, then she needs to stop hitting. Tell her she is not allowed to hit, it's mean, it's hurtful, it's unacceptable behavior (or create your own phrasing), etc. State that "being hit makes you sad and now you don't want to play anymore", she needs to use light touches. I would pull her away from whatever activity or game she is doing and make her play by herself, without the toy or away from whatever it is that she wanted. Also, I used our pets to teach my boys about the pressure of their touch compared to the reaction of the pets. I kept stating the same phrasing of light touches or nice touches, so they could make the correlation.
Additionally, sibling rivalry arises partially from jealously of attention, stuff another receives, feeling of being shorted... even when everything was equal on their serving of cake or they had the same toy, etc. The child needs to see they are loved, valuable and they can do good things to gain rewards, confidence, independence, more affection and to feel they are a special part of the family.
I have diverted quite a few fights lately between my 4 and 5 year old boys by requesting one of them to help me with something or remind them that good behavior earns stars. I started a rewards system, and they gain stars for doing things. If they do well and gain stars in the category all week, then they get to add a block to the rewards chart. They can earn enough reward blocks to go to the Dollar Store, a restaurant, play at the park, have a friend sleep over, go to the theaters, go to the movies, pick out a crazy dinner (of snacks or items I wouldn't normally let them binge on). They are able to spend time with me and they feel more connected to me. They learn new skills and gain confidence. They learn how to problem solve by workiing through frustration on little tasks daily. They are praised for trying and/or accomplishing the task. They earn reward stars and praise: hugs, kisses, reply with a thumbs up, good job, or whatever. Sometimes I give them stickers. The rewards are given to encourage them to try and to ask for help only if they get stuck, want direction and need help (verses the kids' giving up, melting into tears and insisting I take over completely).
I go over the rewards chart with them when they do something really good and at least once a week to tally their stars, praise them, ask them which category their reward block should be placed on the chart and give them a small reward such as candy, a cheap toy, a small craft or activity, an outting to grandma's house, an outting to a store (like seeing animals at the petstore), going on the $0.50 rides at the mall, etc.
My kids love the extra attention, learning new things, feeling confident, and knowing their efforts and obedience are valued. Sometimes just saying "thank you", even if it is really heart-felt, doesn't build energy and rapport to stay in line or to keep putting forth the effort. My kids really look forward to earning stars, and they try to find things to help me. After they do it they say, "Mommy, I earned a star!"
I give them very basic tasks and label them in a category. At this age, basically if they are cooperative and do not throw a fit because they don't want to do it, then they can earn the star. At some point, for each task the task is increased so they have to take on more responsibility without my intervention or monitoring. They have a category of "Dressing", which includes picking out their clothes, cooperating to put them on, putting their dirty clothes in the laundry basket, etc. "Car/Bus" category is for whenever we are going somewhere they cooperatively and mostly independently put on their shoes and coats, carry their own bookbag and bucklet themselves in. "Dinner" category is for them helping me set the table or clear off the table with meals. They have to carry their dirty dishes and put them on the counter. They have to clean off the kitchen table, throw away napkins, push in the chairs, put away condiments or other items left on the table, help me put away leftovers, help load the dishwasher, etc. "Toys" category is for putting away toys, not leaving toys on the floor (to keep the dog from eatting them), organizing the toys instead of just throwing them into any bucket or in the general vicinity of their toy area.
By doing this, it has made me take notice of how hard they are trying. I give them more praise and I try to include them in whatever I am doing. I figure that daily I spend at least 30min making dinner and another 15-30min cleaning up after dinner. They only spend about 20min eating, so dinner time is mostly eating and then they are off playing or watching TV. Less TV and them being alone with each other, even though I was only a few feet away, meant less sibling rivalry, fewer outbursts to pull me away from household duties, and they seem less hyper when they don't have the stimulation of the crazy cartoons and commercials.
We used to spend like 1.5 hours a day in the same area of the house but not really interacting. Now, we spend more family time together even if it's not all relaxing. They are learning to combine fun and tasks. They end up telling me things about their day, things they are learning at school, happenings with friends, and just chatter away.
Most of our lives we are working at our job, keeping our homes tidy or studying for school. We might as well be able to bond through it and enjoy the time as we go.
Well... this isn't a fix, but maybe a different approach could help. My boys have always been very energetic, competitive and emotional. They are always on the move, making up games as they go, but the smallest little thing said or done makes them sad. They feel so hurt and frustrated they act out with yelling, screaming, hitting, punching, thowing things, in other words... normal kid things.
I have been teaching them to identify their feelings, tell the other person how they feel RIGHT AWAY (instead of shrinking away--internalizing the frustration and acting out in rage). They say, "you took my toy, you hurt me, you make me sad, you make me angry," etc. I started with very short phrases, sometimes only one to three words so they could remember. I talk about figures in books, stories and others' situations and ask them "what do the characters feel, what did they do, what should they have done, and then I tell them the right answers. Identify feelings and the problem right away. If then don't listen, speak up and demand again. If that doesn't work, find an adult for help or walk away if it isn't that big of a deal to them.
I have also encouraged the kids to stop rough-housing. I know it may seem a bit easier for me to suggest because I am no longer married, but I dated and have others' input far more than I wanted... this has helped quite a bit. I have used new rules of no jumping, crawling around or plopping onto the couch or chairs. They can hop around and roll around on the floor, but they cannot wrestle with each other. They cannot push or physically be aggressive with each other even when playing a game or sports. There are no aggressive tickling fights, throwing pillows,(or really) throwing anything in the house.
I realized that my kids cannot differentiate between rough play and then becoming mean. They cannot create a boundary and decide not to act out when rough play is out of control. (And if you look around, most adults struggle with this as well when feelings are hurt or someone is physically hurt. Many people result to pushing, shoving, slapping, cursing or being manipulative to get their way.)
I figure that at no time in our lives are we legally allowed or socially encouraged to fight back unless we have a truly life threatening situation. If I force my will on another person, the person is not going to accept it, understand it or be consistent at it. We need to find a diplomatic way to build a bridge for change. Otherwise, to see changes occur you will have to put in far more effort, time, money and other resources to achieve the desired goals.