He's trying to find his boundaries, determine who is boss, and right now he is. So it may take awhile for him to learn that he does not call the shots. I'm old school and my kids knew this at a young age, so I have no answers.....sorry.
He might simply be overwhelmed by the visual stimulus in a store. Some kids are like that, it makes them tremendously edgy. I'd give it a rest, and not take him for a while, and then see if his continuing development makes it more possible in a few months.
This has always been my thinking too. What can we do? We pop his leg, we ignore we have tried everything. I think you could beat this child (of course we never would) and it would not stop him.
I think you should be able to take your child anywhere and expect good behavior. I did with all 3 of mine ages 4 and under and a single mom. I was able to enjoy my children anywhere and anytime. I do think they are calling the shots when I see so many exhausted mothers carrying a screaming toddler out of the store or mall. You have to wonder who the boss is! He is old enough to learn patience amd that sometimes he has to do things with mommy that he may not want to, but this is what life is about. If all he has to do is throw a fit to get out of what he is doing, what are we teaching them?
Maybe you are right. I just took my son everywhere from the time he was born and had very little trouble. However, this baby is a whole different child. I want him to learn how to behave but maybe it is too early to expect too much.
I don't blame his mom. Now that I have a small son, I treasure getting to the store without him in tow. Who says a 2-year-old needs to go to the store? If you don't make a big deal about her going when he is staying home (i.e., if nobody suggests to him, "Well, you got your way, you don't have to go to the store,") he might not connect his bad behavior at the store to the fact that he doesn't seem to have to go there any more. (In case he does, you could start with the "You don't get to go to the store and Mommy does," approach, to counteract it.) If she can arrange coverage for him at home and get to the store without him, this might be a fight worth sidestepping at this point. It's not like he's 12, he's just a little tyke. He can learn to do things he finds boring at another time in life.