I'm glad that everything worked out alright in the end for everybody involved, but if this had happened to me, then I would not have opened the door and gone outside (calling the police would have been a good idea if one has the time), and even if I had then I would not have let the guy get so close before either retreating or firing. So yes, in your place I would have shot him, but only because I had made several consecutive mistakes earlier, hypothetically speaking. On the bright side, you kept your cool and managed to defend yourself without killing anybody, tactical errors aside. Good job, and try to learn all you can from it.
As for the trigger issue, at least the way I train, my finger only touches the trigger when I've made the decision to fire--done deal--otherwise it stays off the trigger at all times because I wouldn't want to trip on something, for example, and accidentally shoot somebody who didn't need to be shot.
I fire from the "finger-safe" position all the time, so it doesn't spoil my aim in case I need to react quickly; I also practice firing strings of shots regularly so that returning my finger to the safe position on the frame is not habitual while engaged in combat.
As for whether I'd leave the house in order to stop a heinous crime from being committed against another person in my own yard, in principle I would, but I'd have to be sure that it is not a trick.
The safety of my family and myself comes first, but I will defend others if I can. Honestly, I'm not sure how I would know that it's not a trick. Based on such cases I've read about, I would view the incident critically for anything suspicious, and finding nothing unusual I might initially use myself as bait, pretending to totally fall for the potential trick, while being alert and ready to shoot, in an instant and multiple times, anybody who tries to rush me, and then I'll turn the gun on the first bad guy. If it's not all a trick, then the perpetrator will cease and desist on my command or else be shot, and if he has a gun then I'll shoot him first. Now I have to go look up state and local laws and case history regarding shooting somebody in defense of another in my yard but outside of my home to make sure that I didn't just say something foolish in a legal sense.