Stranger at the door around 3 AM....

Yeah that's seriously something you need to alert the authorities about and not try to solve with a threat of violence. Who knows? Maybe he's an alcoholic. If you run up and just try to scare him with a weapon, he might pull a gun.

Make a report with the police. I'm not sure why your family hasn't done that yet. And let her stay somewhere else for a while

Machete or a gun stay over and answer door with weapons in hand, tell him to fuck off or die. Friend with you for backup. Or have a friend do it.

Yeah... Don't be stupid. Just stay and give her peace of mind. If the person comes back, call the cops. Threatening violence would do jack shit aside from getting you in a lot of trouble or dead. If push comes to shove, that's another story all together.

I'd invite them in for tea and cookies. Could be a fairy. http://i.imgur.com/yZLzV4g.jpg

Now that the reasonable answers are out of the way, I'd booby trap the door. Maybe an airbag that shoots out. Or a fake welcome mat that leads to a nail pit. Swinging death scythes. Or a band of Jehovah's Witnesses that show up at the same time he does. Or a Justin Beiber poster on the door...