I had the exact problem with my girls, 21 months apart. I absolutely could not leave them alone for 5 secs, even to run to the bathroom, or it would be twice as bad.
I tried to get things they could do together, blocks, puzzles, things to do on the floor. I gave my 2 1/2 year old jobs to help with the baby, bring her toys, water, blanket, etc, and tried to keep her busy. When she did push the baby, which was very often, I would pick up the baby and give the baby my full attention. When my older girl would approach us I would ask her to look at her face and see how upset she was that she was pushed/hit/laid upon/etc. Iwould ask her if she looked happy or upset. Then we would talk about it and I would let her know the behavior was never ok. She was not allowed to hurt the baby, just like I would never let anyone hurt her. I did not shame her, but I was very clear it was not ok, that I would not let her do it, then I would try to move on to a together game, on the floor.
It was a very difficult time and did not go away for awhile. I felt guilty and got very angry. It is so hard to see someone hurt your baby, even if it is your other baby.
I have to say, they are just 4 and 2, and they are each others best friends. I would never have thought it possible, but they play very sweetly, dress-up, babies, tea party, cooking, etc. They still have squabbles, daily, but now it is over toys and not one-sided. And here is the kicker, by baby absolutely worships her older sister and when they are separated they cry for each other (like at preschool).
Lastly, everyone gave me the advice to 1. talk to my older one about her negative feelings about the baby and validate (not approve but so it is okay to feel that way) and 2. spend "special time" with the older child.
Hope this helps, it changes, but it is very hard.
K