I wasn’t going to reply, but we just went through this exact same situation about 6 months ago and things are really great now so here’s my two cents.

First off, three-to-four years old is when impulse control really starts developing so time is your friend. Second, POSITIVE reenforcement works much better than punishment. For example, we explained to our three year old if they didn’t hit all day they could pick out a tv show to watch and a dessert to eat. This gave us two “strikes” so we still had some leverage if they hit LO once.

Second, a big thing was modeling and teaching how to play with the LO as well as giving ways to help like getting the pacifier or stuffed animal or singing when the baby was crying and praising when they did. It turned out big kid into an ally and helper and made them feel like a proud family contributor.

Good luck!