I have two daughters, 8 and 10, and there have been some fighting issues over the years. Things have improved greatly over the past year or two, and I'll tell you what has helped me.
1. Prayer (always #1 on my list because it yields results). Turn it over to the higher authority and pray for wisdom in what to do.
2. Your older daughter needs some special time just for her. Let her know that you need some help with something VERY important, from a big girl, something she would enjoy doing (helping you make cookies, go shopping, or something that she likes). However, tell her that she can't help with this special thing unless she is extra kind to her sister, because she won't be able to help with this. This tactic has worked wonders. I also make it a point to do special things with the younger one, too.
3. Talk about how you always wanted two daughters, because you didn't have a sister. Tell a story about two sisters who grew up being very close to each other, and remained best friends until they died at a very old age. I talked to my daughters about my sisters and me, and shared the story of my grandmother and aunt, two sisters who lived only miles from each other their whole lives, yet their personalities were very different.
4. Let them know that it's okay to have different likes and interests. They don't always have to have the same things. Help them embrace their differences and compliment each other on things. Make it a habit, before dinner maybe, to find something they like about each other before eating (your younger is too young for this but it will work when she gets older).
5. When you do something special for one, like celebrate a birthday, don't completely ignore the other. Remind them that they will have a special day of their own and that sharing in the other's special day will make it better for them when it is their special day. If someone is complimenting the little one (people tend to do that and neglect the older), then turn to the older and say, "and she's my helpful big girl and I'm so PROUD of her, too."
6. The minute your older daughter gets physical, remove whatever she was using from her hand, and take it away for at least a month. Separate them for 30 minutes. Every day that this happens, remind her that night about what happened and why it has to stop. Make a chart where she gets a sticker for every day that she has been kind to her sister, with a reward given to her after so many stickers. This ALWAYS works well for us. No voice raising needed. If she is doing physical things to her sister and picking on her so often that it is hard for her to not do it even once per day, then put a scary, monster-looking sticker on her chart every time she acts more like a bully. When she does something nice, negate the other sticker with one of her favorite characters. Put the nice sticker right over the not-nice sticker. My older daughter went through a brief phase where she would pinch and push. After using the "nice" and "not nice" stickers, the bad behavior improved quickly. The fights aren't gone completely these days, but they are hardly ever physical. If my older daughter pinches, she loses one of her most prized toys forever. I've rarely had to do it.
7. When my daughters were in regular school (they are homeschooled now), there was a LOT more fighting when she got out of school. Pressure to behave well at school (she always did) and being ordered around or dominated by more aggressive personalities often made her want to take things out on her sister. The fighting was reduced considerably when we started homeschooling. Homeschooling is NOT for everyone, but I just wanted to let you know how much it has improved sibling relations for us. They are truly best friends and understand how important they are to each other. In another few years, hopefully your older daughter will start to appreciate her sister more. Because of the bigger age difference, it will be a bit more challenging for them to have as much in common and ability-wise, but it can be done. My sisters were both 4 years apart in age from me (I was in the middle). We are all very close now. You can remind your two that when sisters grow up, sometimes they end up being best friends.
8. A family therapist would be helpful if things don't improve. I was planning on taking mine to one, but things worked themselves out without it. Give it a few months to a year to see if you can help improve things without resorting to the time spent and cost of that.
9. Oh, one more thing. Try letting your older daughter be the "referee" when there is a fight or disagreement. Read books or talk about what is fair with her to help her be a good referee.
10. I agree with the poster who said to keep the little one in your sight at all times so your older daughter will be less likely to lash out on her. Another poster said that they know what they are doing. Kids sometimes thrive on the negative attention so let them know that you're in charge and calmly separate them. Keeping the older one bored in a room might make her less likely to pick on the little sister next time.
Blessings to you,
S.