I'm wondering if hitting is a natural stress response, or something children learn either because they were victim of such abuse, or from witnessing it being perpetrated on someone else?

I am for children understanding boundaries, what is acceptable, what is not, and consequences, but absolutely no spanking, and ideally no shouting, though...

More important than punishment, would be to go to the source and try to understand why they behaved the way they did. Only then can you be effective at preventing it from occurring again