The way with the "real" woman and her "real" daughter where acting, lets just say the living side of the three, that the dead girl may not have any relations to anyone living in that house. The ghost girl could have died in her home, or somewhere else, and being able to move freely around the world. The ghost girl had no idea she was dead.
The Others is a good movie to see for this kind of thing.
Now I'm just throwing this in, but dose anyone have an Idea, at least I do, to who the exorsist might be?