We have a lot of minor shuffles in my house too. The 3 year old pushes over the 1 year old a lot. My older kids hit and push a lot too. So frustrating. Nothing we do seems to make it better.
The grandkids are like that too (6 and 2). Doesn't help that the 2 year old is aggressive and has all the makings of an NFL middle linebacker. But it's disturbing, because it's almost like the 6 year old goes out of his way to hit/hurt his brother. But they generally get along great; it's weird.