If that is too embarrassing for you, you can try simply leaving the store. When your child starts acting up, tell him/her you will leave if you have to warn them to be good again. Then if they test you, immediately and quickly leave the store without saying anything to your child until you are in the car. When you are in the car, ask your child why you left. If they don't know the answer, tell them, and then take them home with no reward in sight.
This one is hard because you only go to the store when you need something. Leaving doesn't seem like the best option but after you have done it 2 or 3 times consistently, your child will realize you mean business and they will change their attitude.
I WANT IT!
Eventually your child will realize that the store is full of things they can have. That realization unfortunately leads to wanting everything in the store. I have also found two things that work for me in this area. The first is to stump your child by countering what they say. For instance:
Mommy! I want that CANDY!
Oh, that's nice. I want a pony.
But MOM! I want it NOW!
I really wish I had a new house right now.
MOM! I want it! It want it! I want it!
You too? Wow! Too bad we can't always get what we want.
This conversation has worked wonders for me with Brooklyn and now she even plays along. After she figures out what I'm doing she will start to say things like, "Oh yeah! I want a unicorn!" Then she will giggle at the realization that she just played too.
Both of my children get really bored when we are shopping. Since Lily is still very young, she can be distracted by simple things like holding my phone or a small toy. But once she figured out the "drop it so mom will pick it up game", I had to invest in some chain links to hold her toys to the shopping cart. I use some that are kind of like the ones below, except they close together better.
If you have children that like to run away and force you to put out an Amber Alert every time you are in the store, then you might want to consider a leash...really! I always thought it was horrible to see mothers with their kids on a leash until the first time I lost Brooklyn. Shortly after, Brooklyn had a pink puppy leash and she loved it! We didn't have to even use it for very long before she learned to stay near me.
If none of the above solutions sound like they would work for you, you might consider shared shopping. You can do this two ways. You can split responsibilities with a friend or neighbor by taking turns every other week either babysitting the kids from both families, or shopping for both families. You simply give your friend your shopping list and take their kids while they shop, then trade the next week!
If you feel like that is too imposing, then enlist your husband! This is my favorite way to shop. Every Saturday my husband and I drag the kids out to the store and take turns entertaining them while the other person fills the basket. Our children love the extra time with their daddy and have finally gotten to the point where they are actually VERY PLEASANT to shop with!