Hi A. -- I didn't have to deal with bullying, but what I did for "uncivilized behavior" might help because it gives some of the responsibility for discipline to the perpetrator.
When one or both of my kids would misbehave I'd say, "Okay, you have to have a 5-minute timeout as punishment for what you did, and when the time is up you can rejoin us IF you think you can be civilized and remember that each one of us is a human being just like you. When the 5 minutes are up, if you don't think you can do that, tell me and we'll figure out how much additional time I should set the timer for. And if you say you can be civilized and you rejoin us but it turns out that you can't be civilized yet, of course we'll have to start all over again, but with a 6-minute time out, and that would make both of us sad." Then I would put a kitchen chair in the hall and sit them so they were facing right into the wall -- no being sent to their room where they could play, etc -- and I'd set the timer for 5 minutes. (Then they couldn't think I was stretching the time out, etc.) Always when that first 5-minute bell rang they thought they could be civilized, and they always
were! And they knew that if they hadn't been successful they'd start all over again (but with the 6 minutes out) because I never made a threat I wasn't prepared to carry out.
I'm not sure how I'd apply this in the outside world but I do know I'd keep a timer in the glove compartment! I guess at someone else's house, daycare, etc, I'd do it like at home with a chair facing a blank wall. In a public place, I think I would have put the child in the back seat of the car, facing the rear. (Guess I'd put a good trashy paperback in the glove compartment too, to amuse myself while I monitored the back seat.) What I did when driving was pull over immediately -- even on the interstate -- and go through the routine, and I'd say "If you're late for soccer, you'll have to tell the coach why" or "If we miss the start of the movie, we'll know whose responsibility that is."
As I write this it occurs to me that I don't think my children were as young as two when I started this, but it worked at three. I wish you the very best, for your sake, but especially for your child's sake, because the person who is most damaged by the bullying is always the bully, and we don't want that!
Onward and upward! L.
Oh! be sure when his brother is involved that he gets the same time out and the same options at the end of the original 5 minutes!