Parents!!

How do you deal with your child if they act up in public places?? Mine is almost three and hates being seated in a shopping cart, we don't let her run around because she will run off and hide which is scary and grab any toy and junk food in site and throw it in the cart. So our strategy we simply sit her down she screams her ass off but my husband and I let her throw her tantrum it takes her less than five minutes to calm damn then she fines. I know we get probably get crazy looks but we don't agree with letting her do as she pleases and she needs to learn right from wrong. So I was wondering how other parents deal with little tantrums in public places??