My sister's 6 year old daughter can be a handful in public. I don't know how my sister deals with it when she's alone with them.
We were in Walmart, and once we weren't in an area of the store that interested the child, she started cutting up, running around with the shopping cart, and just being a brat. I told my sister "Give me the keys". I told the kid "I don't tolerate this crap from children, we're going to wait in the car until your mom and sister are done". She said "Make me", so I picked her up, threw her over my shoulder and carried her out of the store. Good thing she's a skinny little thing.
She is generally pretty good for me, when I'm watching her. I own the thing she loves most in the world (my dog) and I can take it from her whenever I want to.