Re: twins fighting
From my experience with 3 year olds, they sometimes get physical because they are either frustrated about something, or they want attention. Either way, the root cause is that they have some need that's not being met, and it manifests itself with them hitting, because that way, they really get my attention. I give them one warning, and if it doesn't stop right there, I will separate them.
I know it's easy to blow up and get angry at them at that moment, I usually do, but I've found that it's not the most effective strategy. I remember my mom getting so mad at my sister and me when we would fight and she would say that she couldn't stand to see one or both of her kids being hurt, even if it was at the hand of another one. It's a visceral reaction and would usually result in us being even angrier with each other. But if you separate them, then calmly seek to discover what is at the root of the conflict/episode, you can usually diffuse the situation and find that they really want to be together. Usually, one has either been busy with something else and ignoring the other one, who then starts to hit, or I've been busy and didn't pay attention to the signs that they needed something, usually attention. Sometimes, they just see a reaction for a random bump and then think it's hilarious. Those times I need to present them with other options and talk to them about how they would feel if they were the victim.
Kids are ego-centric, for a long, long time, so sometimes it feels like I'm talking to a wall, but then it somehow sinks in. Every day they show further signs of empathy and understanding. I'm starting to ask them to offer suggestions for alternatives, and I couldn't believe it yesterday when my son said he should say "please" when he wanted something his sister was playing with instead of snatching. This would not have happened, even a month ago, if I hadn't been working through this issue in this manner lately.