He is only just-turned 2. His impulse control is next to none. Even if he understands that he shouldn't poke, squish, etc the baby, in the moment it is v. v. difficult for him to stop himself if he has the impulse to do that. This is probably not what you want to hear, but what it boils down to is that it is entirely up to you (not your ds) to make sure your 3mo is safe all the time. You can't leave them alone together. You can't leave baby where big brother can reach him (unless you are right there and keeping an eagle eye on ds1). Wearing ds2 in a baby carrier or maybe laying him down in a pack'n'play will help keep him out of harms way. (Or maybe ds1 could go up on your back while you're doing stuff around the house while ds2 is in a bouncy chair?).
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I don't think this is a situation that warrants punishment at all. I know (trust me - I *know* - I have 2 kids too!) how much the "mama bear" instinct can kick in when your older dc is being too rough with the younger one. It's very difficult not to have a highly emotional angry reaction when something like that happens. But don't forget that a) your ds1 is still so very young, and still at the very beginning of his journey learning how to act and express emotions in an acceptable way, and b) like I said above, in this case, it really is up to you to ensure your babe's safety. Your ds1 is simply not old or mature enough to be held responsible for ds2's safety. At this point it is up to you mama.
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Now, that said, of course you should be working (laying the groundwork!) with ds1 on what *is* acceptable behaviour. You say he is not yet talking and I'm sure that goes a long way towards his frustration. Every time he hits, etc, try to give words to his feelings. Keep it simple. "Ds is mad!. Ds wanted the cookie!" (or whatever... yk). When you read with him point out the characters and what they might be feeling ("that girl looks sad. Maybe she's sad because she lost her teddy bear"). Make conversations about emotions a part of your daily life (talk about your own emotions too). Practice "gentle touches" too (on you, stuffed animals, real animals, baby, etc). Let him know how much you like the gentle touches.
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One other thing to think about is that to help set ds1 up for success it's important that he's well-fed, well-rested, and had enough 1-on-1 attention. Hunger, tiredness, and craving attention (even negative) are all things that can exacerbate the acting-out.
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ETA re. the babywearing... if you're interested I suggest you check out your local babywearing group. They can be a wonderful resource to help you with different carries, how to get carriers "tweaked" just right, and most have a library of carriers that you can try out to find the one(s) that work best for you. It's also a great place to meet like-minded mamas (and, at our meetings anyway, there are often toddlers your ds1's age there too that he could run around and have fun with).