As the PP said, AP holder are usually limited to purchasing two of the AP exclusive pins at a time. You will have to show your AP and ID to purchase the pin(s). I would suggest asking about AP pins at every pin location you stop by. Sometimes one shop might be out, but another might have it.
The last time I was at AK, the pin "store" outside of Island Mercantile (the big shop on the right as you enter Discovery Island from the front of the park) had the AP pins.
There is also the big pin shop in DTD that carries the AP pins.