First, I would suggest you take her to her doctor and have a frank discussion about the way she acts out, just to make sure there is not a medical/biological issue to deal with. He/she may suggest some tests or have your daughter seen by a specialist.
Assuming she checks out fine, the next step is to take a really honest look at how you deal with her behavior. Are you really consistent with consequences for unacceptable behavior? Consistent with praise for desired behavior? I know this sounds basic, but it really is key. Her actions sound like temper tantrums. Does her trouble at school arise when she doesn't get her way?
It may need to get some assistance. Make an appointment to speak with her teacher and have a frank talk about your daughter's behavior at school and home. Perhaps a school counselor or resource specialist can sit in too. Together you can come up with a re-training plan. Write down specific behaviors that need addressing and come up with apropriate and enforcable consequences for each. Also make a list of desired behaviors and come up with reasonable rewards for consistent obedience. Star charts work well at this age. Earn stars for nice words, kindness to her sisters and school mates, obeying you and her teachers 1st time, homework/chores done without whining, etc. Take stars away for tantrums, disobedience, etc. Once you have a plan that all of the adults in her life can help enforce, let her know the new deal. Make sure she understands the rules and how she can earn stars (X stars at the end of the week = reward,or whatever you decide) and what behavior will get stars taken away. Always give one (only one) calm but firm warning for unacceptable behavior. " Mary it is not ok to yell at your sisters. You need to stop right now or I will take a star off your chart and you will have to sit on a time out." If she continues just calmly take a star off the chart and take her to the time out spot. If she is a head banger, make the spot in the middle of a room. A simple bath mat can serve as a spot. If she gets up, put her back. She's 7 so her time outs should be 7 mins. This is really hard and she will continue to test you. She knows if she throws a fit and bangs her head and breaks things it upsets you. Stay calm and just keep putting her back on the spot for as long as it takes. (timer starts over until she sits for the whole 7 mins) When time is up, she should apologize for disobeying/yelling whateve and you should forgive her and give her a hug. This could take all day the first time, but stick to it. Her well being is at stake. Ask another mom to help you. Not necessarily come over and put your kid on time out, but be there on the phone to help keep you strong. You have a strong-willed little girl and you really need to show her you are stronger! When she earns stars make a really big deal about it. 'Mary, I really like how you are playing with your sister. You get a star for that!' Make sure you are really showing her that life is good when she behaves and life isn't so good when she acts up. Words will not work at this age. Actions work. What you do,not so much what you say. :o) Stay strong! This will be a long process, but soon she will learn that you mean business and all the yelling/kicking/throwing things isn't going to change that. You are unshakable! Ultimately this unshakable mom will give her the stability she needs to settle into herself.
May God bless your family, and remember you are not in this alone!