Kids act out in public. Not every time they’re out but sometimes it would appear that the moment you unbuckle them from their car seat, a switch flips and you are in for one doozy of a shopping trip. The kids start to running, screaming, fighting, and crashing into unsuspecting victims of their rampage. It happens.
Don’t leave! Not because of other people, at least. Keep shopping. Your kids need those trips and they need to see how you interact out in public with OTHER people. Do what you can to stay calm and when people scowl at you, snap your focus back to the task at hand. If they make comments to you, smile, grab that bag of chips and move on. Those people were jerks as kids and don’t remember the hell they put their poor mother through anyway.
You don’t owe them an explanation. Use the trip as a learning opportunity for them too and remember that karma’s a bitch.