A: It is great that you appreciate how spanking isn't the answer--it only makes children more aggressive. The reason is exactly as you say: small children want to do EVERYTHING that the big people do. Spanking children makes them feel like hitting and making someone else suffer as soon as your back is turned.
I suggest that your goal is to try to keep the peace, to prevent problems as much as possible, and to separate the two brothers when they squabble. A play pen may help you establish a physical distance until the conflict settles down. You can interrupt disputes by offering a distraction, picking up one child and moving him away, or providing an activity that they can both enjoy. You can say firmly, "No, no, no--we don't hit" and interrupt the battle. A stern look conveys your message as effectively as anything can. I think that a "time out" on the lap of a soothing adult can be helpful to a toddler in the midst of a meltdown, but trying to put a child into a "time out" somewhere else as a punishment usually doesn't work.
You are right that "frustration" is really the issue. Restoring calm as quickly as possible is probably the wisest path.
Elizabeth Berger MD
Child Psychiatrist and author of "Raising Kids with Character"