In my opinion the question is superfluous to the particular example, though surely it has its place elsewhere. See, you clarified your own and the neighbor's dog's position. What they need (security of territory/safety of pet) and what is in the way (an invader/an aggressor) of that. So both you and it reacted in what you immediately judged to be the most effective action at that time and we can go on discussing justification for either side for another three pages.
Now, why do you need to call anything in the given example good or evil? It serves not to make the situation at all clearer. At best, these labels draw an even sharper divide and serve to overly demonize one party while overly glorify the other. If anything, labels like good and evil would serve to justify even more violence than can possibly be required to resolve the situation.
As to the main questions you pose, I'd say the labels are not so much relative as they are subjective, as necessarily all labels are. A single isolated thing can at the same time be neither good nor evil but it cannot be both good and evil. In other words, there is only one side of the middle ground there, something we'd call a discontinuity. Now, can violence be justified? Probably. Depends on what we mean by violence, can and justify respectively. Saying it's either good or evil though doesn't do much to either justify or condemn it. It just makes the approach sound... simplistic, if we want to avoid calling it childish.
Better to leave questions unanswered than answers unquestioned
