Ah, here I come to play devil's advocate again...

First off, I think this lady is as much to blame as the officer, if not more. She knew Trouble was aggressive before he came around, and he had already attacked the dog she says she couldn't live without, so it seems she didn't love the dog all that much if she didn't even protect it from a known threat like Trouble. Also, the officers didn't do anything on the 22nd because there was really nothing they could do. She told them the dog was someone else's property, and it really isn't a cops job to get rid of unwanted pets. When she called them back, though, the dog had injured a human and this woman wasn't even smart enough to clear her kids out, or even seperate it from the dog it had apparently repeatedly tried to kill. As far as I am concerned, this lady does not come off as a real rocket scientist, or a real concerned pet owner. If she was worried about her beloved Tigger she should have called animal control at least by the time the first attack happened and reported the dog as abandoned.
As far as shooting the other dog goes, there quite simply had to be SOMETHING more to the story than this woman is telling for an officer to open fire in the house. He shot the first dog because he was told it was a danger to the people in the house. He was protecting them. And while that was happening, the other no doubt blood-spattered and extremely agitated dog lunges forward towards the officer and children. I know we all love animals here, but I hope to god that I am not the only one who, if forced to make a split-second decision between what could be the life of a dog and the life of a child, would have to err on the side of saving the child. And lunging towards the officer is not a disgracefully poor excuse in MY opinion. The physical ability pits have to cause immense bodily harm is not something to be taken lightly or that we can pretend doesn't exist just because we know sweet pits.
I just think there has to be a lot more to the story than this lady is telling. I'm not ready to lynch the officer yet.