You do see a lot of these stories but that's because they make the news at a ridiculously high rate, even if the cops didn't do anything unnecessary. In this case they were absolutely in the wrong. They're there to deescalate a situation, not take it over the top and put lives in danger.
By and large, reporting on police officers is a lot like the "how's my driving" stickers on the back of semi trucks. Nobody calls in to compliment the guy for properly signaling, staying centered in the lane, or moving over for the traffic coming up behind him. People call in to complain about the driver who just cut them off, was driving erratically, or refused to move over for passing traffic while driving 5 mph under the speed limit.
People don't report on all the times where cops do a good job or handle their duties as they should. They report on all the times where cops do something stupid like this.
There were 800,000 sworn police officers in the US in 2010. You could get 100 events of varying inappropriateness per day for the entire year and you'd have about 4.5% of the national police force giving the other 95% a horrible reputation. While that would give you far too many acts of misconduct, 95 out of 100 guys not behaving in that manner is pretty good. Get rid of the offenders and move on with the guys who do things the right way. Part of the problem is, once a person has secured a government position of any level it almost takes divine intervention to actually get rid of them. What you have a system who's hiring standards are likely a little lower than should be, but who's criteria for termination are entirely too high. You simply can't get rid of the bad eggs fast enough.
While I agree that this sort of even should never happen, the reporting in general is incredibly biased and really is a disservice to the honest and hard working police officers who handle their job like a professional day in, and day out.
Was the driver in the wrong for driving away? Of course. You're an idiot for arguing a ticket even if you are entirely right because you are in a no-win situation and will only worsen your current predicament. If you have a legitimate gripe with the ticket, handle it as you should even if the means to do so are entirely to inconvenient, more often discouraged by the cost to fight it, and the process is mostly unnecessary.
That said, the officer here had the entire wrong approach after she took off and then stopped. First off he should have had backup. Any time a routine stop ventures outside of the realm of "routine", there should be another officer at the scene to help moderate both the citizen in question but also the officer involved. When the woman takes off, the cop probably got a hefty dose of adrenaline and since he's all amped up when the lady finally stops his first move is to open her door, start screaming and try to pull her out. He should have called for backup and waited not only to allow the situation to mellow a bit but also because he's putting himself into a position he cannot handle. He can't control the passenger side of the vehicle and luckily for his sake it was a car full of children and not a car full of grown men with bad intentions.
Had he waited, the other officer would have pulled up and observed what looks to be just a routine traffic stop. Of course he'll be aware that it isn't because he's been called out there to pursue a fleeing vehicle but I think it's safe to say his nerves are going to be a little less on edge than those of the guy who was actually chasing after the van. They approach the care together and none of the kids sneaks out the passenger side, turning the entire scene into a complete circus. The cop was literally in over his head at this point because now he has two people with whom he needs to gain cooperation from and he's splitting his attention between the two by chasing after the kid. To top it off he starts clubbing the window on the side of the car where the mother isn't seated and where a handful of kids are just sitting there watching it all unfold and this isn't even the worst part of the whole situation.
The worst part is Barney Fife shows up and without having seen how it all unfolded and possibly not even aware of who he's shooting towards starts shooting at the car full of children.
Just a dumb situation made by possible by poor decisions on both sides of the fence. Was the lady in the wrong for driving off? Absolutely. That doesn't mean that the cop is defaulted into the "right" position. There's a right way and a wrong way to handle any situation and he handled this one poorly. He took on a situation that was beyond his control and when chaos ensued he resorted to beating the hell out of the van while another cop who was late to the party went straight for his weapon.