Researchers secretly watched families with children to find out what discipline looked like outside of a laboratory. The real observations they made were of discipline in a public setting, as I imagine discipline in a home setting would give very different results.
They sorted categories of discipline with good touch and bad touch. With bad touch including arm pulls and pinches.
Many parents have told me they feel embarrassed when they are in a public place and that embarrassment leads them to those bad touch situations they later feel guilty about. It is very common, but not necessary to feel this way. The strangers around you have no idea what kind of stress you or your child is under. Staring eyes may feel like judging eyes; they may be judging eyes, but you are the one in control of the situation.
Your child is still learning appropriate behavior. Take that deep breath. If you are trying to conduct business, go ahead and let the cashier roll their eyes when you tell them “just a minute” so you can attend to your child.
Remember that sometimes all your child needs, is for you to acknowledge the message she is trying to give you!