Sometimes it is necessary to use deadly force if you feel your life is in danger. As the girl herself said, had she not feared for the life of her child, she was unsure if she would have pulled the trigger. Even in the UK, despite a lot of confusion over what our rights are with regards to self- and home-defence, this would almost certainly be treated as such.
That said, it seems strange that no alarm bells were set ringing by the death of the dogs, was this reported? Did she mention the 'creepy man' at that time? Not trying to say that anything could have changed what happened, it's easy to judge in hindsight, but you would have thought someone at the PD would have at least thought, "we'll keep a patrol in the area for the next few weeks, because something is going on...."