According to CollinsDictionary, pacifism is: (1) the belief that violence of any kind is unjustifiable and that one should not participate in war, and (2) the belief that international disputes can be settled by arbitration rather than war.
The second definition seems rather narrow to me, so I'm going to stick with the first one. I'm also going to limit this to violence between people. Violence towards animals is a whole subject of its own, and I'm not going there today.
Some of my readers might think of themselves as pacifists, and others might be nothing of the sort, so hopefully that will bring a whole spectrum of views to the table.
So what we're talking about here is this. If someone believes that violence of any kind towards other people is unjustified, what would it take to make them pick up a gun and use it against somebody else?
So what should a pacifist do in that situation? Obviously they would seek out every non-violent means at their disposal to save their loved one, but how about if I pose a more specific problem, and we'll see what we can do with it.
There are several things you don't know about the intruder. Are they armed? Are they willing to kill? Will they kill without hesitation, or would they negotiate? Will they find you in the next ten seconds or ten minutes? You simply don't know. Will you leave it to chance, and hope they won't respond to your presence by killing you and your loved one? Or will you act first, quickly, and take chance out of the equation? Hit before they know you're there? Kill first?
Perhaps then the dyed-in-the-wool pacifist might respond with violence?