I can see maybe they might have stopped the vehicle based on the earlier report (which was somewhat ambiguous but may have had an inkling of something strange going on with money flying about) just to clear things up, but given the circumstances, a family (with kids?) traveling with (non-pitbull) pet dogs, then obeying orders and doing what they were told, well, it would seem that even the most intellectually-challenged cop could conclude that there was likely no threat here.
And I don't see any justification for killing the dog. Cops kill a lot of dogs nowadays because they are trained to do so (i.e., JBT training) and they know there will be few, if any, legal repercussions to their getting their jollies by firing off their weapon and killing something. Unless that dog was on top of the officer doing him some serious harm, I don't see how killing it is in any way justified.
I agree the cops probably weren't concerned about reprecussions when this happened. Perhaps when a jury comes in with a million dollar verdict against the Sheriff's Department somebody in authority will clean house and, when the new policemen are hired, will explain they can't act like Jack-Booted-Thugs without severe personal reprecussions.