Rather than scolding her in public, try these methods to get her to behave instead. http://www.parenting.com/article/toddler-discipline-tricks-work If you have to chide her, squat down and look at her at eye level instead of looking down at her. Talk in a firm tone, but don't raise your voice. You may say something like this "Mummy feels hurt because you refused to leave the store when I asked you to". It gets her to empathise with you instead of feeling sulky about getting scolded.
Please do not shame her/him in public as this is very hurtful. They are little human too as adults never like to be scolded openly. What you can do is to do firm voice and set boundaries with her/him. You can use reward or consequences for her/his misbehaves.
Definitely not a public screaming match, maybe take her aside and explain what she did wrong? If she does not calm down, tell her that the outing's over, fun time will end and everyone has to go home. Works for me.
It's not okay if you believe that correcting a child shouldn't involve embarrassing her. It's best you take her aside, outs of earshot, and then explain to her what she did wrong and how you expect her to behave.
thanks