Had either of the parents or the son suddenly bolted upright in an attempt to either stop the officer from shooting the dog, or in an attempt to shield the dog, I have no doubt that the officer would turned and fired killing them.
His reaction to the dog was totally unjustified. He appeared highly on edge for someone toting a shotgun at shoulder level ready to fire. The people in the car had already been restrained. Street smarts alone would have immediately told any responsible, experienced cop that something was wrong with this stop.
These people hardly fit the profile of someone who had just robbed a convenience store or committed a robbery.
The officer should be fired. This is the kind of guy who breaks down a door at the wrong house on a drug raid and proceeds to the backroom and blow some confused innocent person to hell. He doesn't belong on the street.
What profile would that be that you had in mind?