When you say that your children were being a pain to you and only you that does not seem to be the case because someone else in a public place aka store overheard whatever was going on and felt that instead of someone else going to a manager (complaining) saying kids were making a mess or whathave you.
She did her job and corrected your children. I have been in a few stores recently, when a sales clerk did. One was a clothing store and there were 2 young children running and yelling around the store as their Mother, grandmother and Aunt were all there watching Mom try on clothes.
The cashier asked the mother to please not let her children run around the store. She stopped taking care of a customer walked over and asked her nicely and politely. After another 10 minutes of nothing being done.
The cashier yelled at her children. They were running in and out of clothing racks bumping into people etc.
She had every right to do so. That is a public place and it is her job to keep things under control in her store.
So should that mother be upset and throw all the clothes that she was trying on at her feet and say you take care of it, you can't talk to my children like that?
I also remember the old saying you break it you bought it. I have also seen many kids break things and parents don't do anything but put it back and walk away. If that was me back in the day...Whoa nelly I would have been in BIG trouble and probably gotten a spank.
Also you say you wanted to teach your children that if someone messes with them, they need to stand up for themselves. Now that I understand completely and I do agree with you, but when that someone is an adult who is asking them to respect something that isn't theirs is a totally different lesson.