How much personal time do you spend with your daughter? Sometimes our schedules get so busy that we neglect spending "quality" time with them. Our kids will "act-out" when they are being neglected. Whenwas the last time that you have done something with this particular daughter only.
How much time do you spend praising what "good" she may do. Kids react to our actions. If all you do is complain and find fault, then she will have no incentive to try and "please" her parents.
Have you considered that she may be dealing with sibling rivalry? Again, when other children come along, we expect our older kids to move over and make room for the next one. This creates fear and instability in the minds of a child that was once in first place.
Maybe you need to change her diet. How much sweets does she eat. Believe it or not but foods can create problems with our kids.
Also, to get her focused on other things, find small projects for your children to do together and things to do separately. Give your daughter responsibilities. Make a chart so she can see all that she has accomplished. Give her books about animals and read them to her, especially the books with mother animals and their babies. Help her see the sweetness of animals and how gentle we need to be around them.
Lastly, be consistent in your punishments not just with your daughter but with the other children as well. And beyond all else, don't show favoritism. I know it is hard to do, especially when you feel like you want a refund on one of them.
Your daughter is not a lost cause. You just need to "listen" to your daughter. And taking a line from "The Lion King's Timone and Pumba" - Look beyond what you see. You can learn a lot from what your kids are not saying. Rita