I don't really think it's acceptable to smack your kid across the face or spank them in public... Like, I think most people have a problem with that.
But, parents interact with their children very differently than two adults interact with each other. Like, if a parent gets stern with their child, say like scolds them or tells them they're going to be punished, that's pretty normal. BUt if you got stern with an adult or told them you were going to punish them, when they're in your checkout counter, yeah, that wouldn't be a normal thing for you to do. Why? For the same reason that your mother telling you to eat your vegetables is normal, but a stranger at your retail job telling you to eat your vegetables is not normal.
Parents do lots of things with their children that retail employers should not do with strangers. For instance, if you work in clothing retail, parents usually accompany their children into the dressing room to try on clothes. But, you as a retail employee should not follow a parent into a dressing room. Parents often take their children to the bathroom at a crowded mall. But you shouldn't take an adult to the bathroom. Parents might hold their children's hands when crossing parking lots, but it'd be a little weird for you to run up to your adult customers and hold their hand to walk them to their car.
