K.S.
Definitely listen to TracyA's advice. Also think how to phrase things from the positive viewpoint rather than the negative. So instead of saying' "Don't pinch your brother", you should say, "Gentle, pat, pat". In other words tell them the action you want, not the action you don't want. It takes some practice to retrain your brain but it works much better.
One thing noone has mentioned about tantrums. A child younger than 5 has a brain with lots of extra neural connections (they get trimmed from age 0-5) and they aren't fully mylenated (insulated) so many tantrums are basically a "short-circuit" in the brain rather than a conscious attempt to manipulate a situation. That doesn't mean you need to give in to them (since that will train the child to use them later in life) but it helped me to understand them and not try to punish the child for it. Keeping them well rested and well fed at this age goes a long way, but also expect there will be A LOT of tantrums as they get frustrated trying to communicate their wants and needs to you but have no words. Teaching sign language can help a lot at this age (start with "food" "water" "milk" "more" "all done")