Shooting a looter I think is a little bit excessive. I would threaten them, and if they didnt back off I'd probably fight them out. If they pulled a weapon like a knife or gun and threatened my family, i would shoot without question.
Now theres a fine line between what I would do and whats allowed. Here in Virginia there are strict laws about issues like this. One says that to have legitimate reason to shoot a trespasser: your life or someone else's must be in danger. That means you can shoot the guy if he points a gun at you, but you cant if he steals everything you own without a weapon or physical harm.
Also, if there is someone standing on the other side of your door pointing a gun through it, you can't shoot through the door. You must first open the door, then you "know" your life is in danger and may shoot.
So, what I would do probably would have more serious consequences than getting some of my valuables stolen. But I definately wouldn't let someone doing that get away lightly.