
I would first ask someone to hold your dog, as you go talk to this person. If you go over with your dog, then she is just going to pick her dog up straight away. Also, dont do it infront of everyone, as she may get defensive.
Ask her how she thinks it is helping her dog to be picked up. Not in an accusing manner, just generally. She may have a good reason, maybe she was told to do this by the breeder. I dont know. Listen to her side of the story. Dont just go over with a lecture.
Then tell this person, that at a dog show, there are quite a lot of dogs, and even in the classes there are hopefully a good sized entry, and she wont be able to pick her dog up there. The dog will have to learn how to behave with other dogs, or it wont be a show dog.
If your dog is calm, and you and her can agree, then ask if it would be alright to take your dog over for an introduction. Or you could suggest puppy socialization classes.
HTH