if they are on the other side of the door and you tell them to not enter and you will shoot if they do then i think you are justified in shooting. but if you just hear them walking around out side the door or you warn them not to come in and they don't, then you probably can't be justified because even though they entered your house and maybe took some of your stuff if they leave you alone or dont try to initiate violent contact then you probably don't have grounds to use lethal force.
if someone is hacking a hole in the door or trying to bust it down and trying to get you or your family and have said they are coming for you (and not just your stuff) after a verbal warning then you
might be justified in pulling the trigger.