Banning kids may be harsh but screaming at a neighbor's child is extraordinarily foolish, especially when you know their parents and can just as easily take it up with them like a mature adult would. I'll never forget when I was a kid, I was riding my bike on a pile of construction dirt in the street outside of some cantankerous crank's home. He yelled at me and a friend of mine and told us to get the hell out of there. (same age as as OP's kids, actually). My father tore that son of a bitch three new assholes, which is the proper way to handle someone screaming at your kid over something as stupid as spitting gum in the grass or messing up the dirt in the street.
You don't scream at someone else's kid unless it's an emergency; handle situations like that like an adult. Don't agree with me? No problem. Gamble all you want.