As unpleasant and worrisome as this may be, it most likely is a phase that will pass. This kind of behavior is typically triggered by jealousy of the baby (don't ever leave the two alone together!!) and, yeah, it is a little extreme.
But don't just take it from me. I put your question to child psychiatrist Stuart Goldman at Boston Children's Hospital. Here's his response:
"Aggressive behavior in toddlers is not uncommon, nor is sibling rivalry or jealousy. In this case you have more than is typical, but it is important to realize that 2 .5 year olds don't really have a good idea of the seriousness of the behavior. The issues are around keeping the infant safe and addressing the behavior and the feelings behind them....[I]ntervening without undue attention is key."
Goldman recommends reading children's books on sibling rivalry, especially, "A Baby Sister for Herry Monster," to which I would add, "I Love You Forever."
Goldman also suggests making one on one time with the toddler when he doesn't have to share mom or dad. Label it, "Mom and X's Time," and make sure the baby can be cared for by someone else, if need be, so that their time together really is sacred.
When family and friends visit, Goldman writes, "Try to insure equal attention is directed toward the toddler when they visit," not to the baby.
Finally, Goldman concludes, "The parent should reassured that this will pass..."
I would also add that when you are in public, take these three steps:
Before you go, remind him the rules of behavior: "When we go to a playground, the rule is, we keep our hands to ourselves." Show him what that means.Tell him, "I'll be there to help you."
Keep a close eye on him and be close enough to him that you can swoop in if you see something that might develop into a situation. Hold his hand or his arm or his whole body. Get down on his level, look in his eyes and repeat the rule. Distract him with something else.
Set low expectations. Leave the activity BEFORE anything negative happens, even if it's only been five minutes since you arrived. That way, you can praise him for his good behavior which will be reinforcing to him. Next time, stretch it out for seven minutes.
If his behavior gets out of control, stay calm. Don't scream or yell at him. Instead, pick him up, literally, and remove him from the action. Say simply, "It's time for us to go home now." He'll protest. Don't try to talk to him, he can't hear you. Later, after the meltdown, you can ask him, "What's the rule for the playground? Do you remember?" and, "We had to leave because you forgot the rule. Maybe next time, you'll remember."
Similarly, have conversations at home about how to talk and touch the baby: "The rule is, we touch the baby gently." Show him by holding his arm or hand while he makes nice to the baby's arm. Keep it positive. If you feel him tensing or winding up, remove him. If he does hurt the baby, show that this is not acceptable by quickly removing him from her proximity. Lift him up and put him down elsewhere: "You can't be with the baby if you can't use the Gentle Rule."