Shopping can be an overwhelming experience for babies and young children. Children may be overstimulated by stores, and misbehave in response to this overstimulation.
It's not always easy to discipline a child while others are watching. However, it's important that you try to be consistent with what you would do at home. Often it may seem easier to look the other way or give in to a demanding child, rather than deal with it right there. However, inconsistency may encourage even more demanding behaviour in the future.
Here are some strategies you can try when going out, in order to prevent your child from having a tantrum:
Try to remain calm and maintain firm limits from the beginning to the end of the trip.
Talk to your child while you shop, run errands and so on - engage her attention. Ask her opinion, and ask her to help you find what you are looking for.
Allow your child to participate in what you are doing. For example, if you are shopping, let him help pick out the fruit.
Don't go on an outing when your child is tired.
Try to keep trips short.
Bring a snack along to make sure your child does not become hungry, and so you won't be tempted to give your child a treat in an effort to stop a tantrum.