We never have problems with our brood in public, either.
When people ask us how we do it, our answer is simple:
In our house, the reward for good behaviour is no punishment.
Everyone over 65 nods approvingly; most people under that age are shocked!
Hi, Alice! I tell people that when you're outnumbered like we are, you have to keep order or go insane ... especially when you're homeschooling.
Speaking of order, it's already 7:30 and I've only seen one child so far ...