I have to agree with Perky to some extent (not too keen on the manipulating part). And if you can't say no to your kids when they ask for things you don't want to buy or don't want them to have, you've got bigger problems than grocery bills.
I've always taken DD along and it's fine. She sees me reading labels, she hears me talking aloud about choosing organic foods, and she has input on what we buy when there are choices to be made.
Also, I agree with the article when it comes to shopping around. I'm not going to drive across town to save 50 cents on something. Now, if I was already in that neck of the woods and I knew that there was a good sale on something I buy regularly, that would be different.