Sorry for not reading this earlier.
Even when my kids were little, I felt it was important to teach the lessons. In your situation that would mean I would have gone to the oldest child and said, "no pushing. if you do that again it will be a time out." Next one, it is a time out (just short, like 2 minutes at that age). When they say, "but he wasn't hurt!" you can answer, you are right, this time he wasn't hurt, but next time he might get hurt, and the rule is that pushing is not allowed." Eventaully you start talking about the whole realm of using physical means to get what the child wants, and explain that none of it is OK, and that time outs will happen. When they are little, they can't differentiate between actions that will hurt and actions that will not, ones meant to be fun and ones meant in anger, so they must learn to keep their hands and bodies to themselves, in my experience. It is super important for preschool and the playground, too.
When they get older and can start to understand some grays, you can slack off a little and see if they can work it out among themselves.
I have a scar from a toy my sister threw at me when she was two. Serious injuries can happen without mean intent. You have to teach them a gentle but zero tolerance policy on physical aggression, IMHO.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).