I know a lot of people who carry their dogs instead of having them walk in stores because their dog has that attitude and it doesn't come across great when they're first meeting a dog.
Molly is that way... She can be a complete jerk and it can never be taken out of her brain to not be like that because she is a little dog. She wants a bigger dog to know that she is the alpha. When you have a dog that has an alpha personality, you never want them to confront a dog face-to-face unless you do it slowly... If not there will be a fight
I always put Molly in the cart when we go to a store. That is her safe zone and she knows that she is safe inside the cart.
Jolene on the other hand doesn't really have that alpha in her even though she's been challenging Molly but she doesn't do it towards other dogs that are not in her pack. Jolene loves playing with other dogs.