Appropriate, I'd probably say so... legal, doubt it...
If this had been a police officer who chased an armed robber and dealt out the "approrpiate" response to these jackasses, people would be calling for his head...
Actually, no. The robber fired a shot which almost hit one of the victim's family members. You know that deadly force can be used to stop a violent fleeing felon, so shooting at least one of the robbers would have been entirely appropriate, and even expected.
As far as the family kicking the dog **** out of the robbers.....well, I'm sure that they were resisting a lawful citizen's arrest. Seems appropriate to me.