Okay, I missed this thread somehow and should probably leave it alone, but I can't help but add my two cents in here!
To me, the defining line is whether or not the woman, her child, or her yorkie were still in danger. The article is very poorly written, so it is hard to discern. Even, if it were well written, it would still be hard to comprehend what really happened. I always belive that in a two person situation, there are three sides to every story -- what one person thinks happened, what the other person thinks happened, and what really happened. This is because we all can view the same thing from the same angle and recount totally different versions of the facts. This is a well known fact and is demonstrated regularly.
From what I can get out of the article, the woman approached and strangled the dog after her child and the yorkie were inside and safe. If that is the case, then her actions were retaliatory and not defensive. Retaliatory actions are illegal and as such, the woman should be punished. Had her actions been defensive (i.e. she was defending her life, or the life of her child or yorkie), then they would have been legally acceptable, though perhaps morally questionable to some.