I have this problem too. I think the older children somehow figure out they have "power" and get crazy weilding on anyone "weaker" than them.
When things seemed to get really bad at our house, I started separating them, and made both of them do a "time-out" in their rooms. I don't take sides. No matter who is right or wrong, who started etc. I make punishment uniform. In addition to a time out, if a toy was at the center of the issue, the toy or toys get put away for a time-out too. If touching, pushing, shoving or hitting was an issue, they'd have to make up for it by doing something nice for each other, and most important they have to apologize for what they did..and be specific in their apology, like "I'm sorry I called you pointy-head. I know its mean to call you names and it hurt your feelings. I won't do it again." Then they have to shake hands or hug. As for something nice to do, I encourage them to pick up the other's toys for them, or make them a card, etc. Sometimes, if they're really bad and did something horrible, I'd make them do a "report" on why the behavior of the day is bad, and how it affects people. I'd do this after I give them the "lecture" on why their behavior is bad. Then, I'd have them draw a picture, and they have to summarize what they learned by explaining the best they can how "hitting" for example is bad, hurts people, and they won't have many friends etc. They give the report to the whole family, and then do a public apology to the family.
If its a name calling thing, each child is given a bank (clear jar) and fined .25cents (it comes out of their allowance) for each time a mean thing that is said. At the end of the day, they can see just how "mean" they've been by the number of coins for rotten words that have been collected. The punishments comes when they have to put their money where their mouth is and forfeit the change collected to the person they offended.
If the taunting starts up no sooner than a completed timeout is finished, they go back to time out but I add more time. In the beginning they'd wind up in their rooms up to half an hour or more. But after a few times in the bedroom sitting on the floor in one spot without being able to get up, move around, read or play etc. they get sick of it, and things will shape up. I know the 2 yo is still a little young to be articulate and verbal, but they can do it in their way. And its good to make them accountable. They get it, and learn. My youngest is screecher. I've even had store security check me out after my two went at it once. But the youner seemed to improve on the screaming front. I think it was his defense mechanism because the older child was too effective in "bullying". But these things I've tried really did help them both work at controlling themselves. Their at least aware their actions effect everyone and that is not good.
