You know what. I don't know what the whole situation was. But from the officer's point of view. You have to think about it. He's pulling over a speeding vehicle that's apparently even ran a red light. It doesn't matter what their reasons were for running it. The officers's standpoint is this, because more often than not a person driving a vehicle that's speeding and running red lights carelessly is that this person could very well be an extremely dangerous individual. He drew his gun in the first moments of the confrontation and rightfully so. I dunno about you, but if I was in his situation do you think im going to believe "My mother is dying." right off the bat. Hell no, I sure as hell wouldn't want to be distracted by feeling sorry for the guy only to have him pull a gun and shoot back at me.
Even if that wasn't the guy's intention. As a fellow law enforcement officer, you simply can't give in to softness just because of what someone says. It could easily be a distraction tactic. Those guys have to put their lives on the line and this guy did what any other officer given the situation initially would have done.
Sure, it's a very unfortunate situation. But this officer was just doing his job and being cautious in order to protect his own life. They really don't get paid enough money to do their jobs (cops/police).