Hurting a kid only teaches the kid to hurt others. If you have a screaming, kicking kid there, then restrain them (basically, hold in the lap or something so that they can't hurt themselves or others), and if it's a public place, remove the kid from the scene and the next time don't take the kid with you. The only time swatting a kid is allright is when you need their attention NOW because they're about to hurt themselves. For example, if a kid has decided to try patting the nice hot circle on the stove, it's all right to slap their hand in a don't touch-way. (Or even better, let the kid touch the hot stove. That way they'll learn not to try it again. ;)) Hurting kids as a punishment also makes them really good liars; if telling the truth results in a spanking, then the chances of a spanking decrease if the spanker doesn't know the truth.
My way would be simple - nice kids get to do nice stuff like visit their friends after school, desserts after eating their veggies, trips to Disneyworld et cetera. I mean, stuff normal kids get to do without causing extra work to the parent/guardian. If the kid behaves badly, then they don't get to do all that. A misbehaving kid doesn't need dessert and they can't visit their friends or the Disneyworld with the rest of the family because they don't know how to behave. Et cetera. And oh, nice kids should get to hear that they're nice kids who know how to behave, because kids need attention and ignoring the nice and quiet kid is only going to teach them that if they behave nice they'll get ignored. Nice kids with good grades get pocket money - bad kids with a line of D's don't need it. And of course, it's OK to lie to kids a little. Telling them that not wearing a seatbelt can take them to a horrible prison where they won't have any dessert or toys is all right in my opinion.
For the little kid in your 1st message, I'd recommend the "you didn't know how to behave"-punishment; the next time you're taking the kids somewhere nice, he stays home