Welcome to the joys of parenting multiple children. I have only one, but I am the oldest of seven, which is a direct cause to the fact that I have only one.
I learned these tricks from watching mom do them. Spend special time with just your older child, maybe while the younger one naps. Encourage your daughter to use her words instead of her hands. If/when she does hit, have her rub her sister's arm, while telling your older daughter to use gentle hands. And last, put her in timeout when she hits or otherwise hurts her sister. I know that you don't want to punish her and make her think that the baby is more important. However she does need to learn that she can't hit, and that her actions have consequences. She can sit in timeout 1 minute for each year old, +/- one minute, so 2-4 minutes for a 3 year old.
Timeout should be some place where she won't have toys or anything to play with,and no attention from mom or dad. My parents used the steps to the basement. When I babsyit for either of my neighbors, I use the refrigerator. The kids can sit there, and I can see them, but I'm not engaged with them. Some parents have little chairs that they have sit in corners, either facing the wall or facing the room.
Good luck. It's a hard row to hoe, but I'm sure you can do it. Hang in there. And remember, a child telling you she hates you, or doesn't like you anymore means that you are doing your job as a parent. As I tell my son, I am not here to be your friend, I am here to be your parent, and if you can't control yourslef, I will have to help you.