In the OP's circumstance, I also believe the top of the stairs would offer the best defensive position.
While hunkering down in a closed room does have advantages, I believe my chances are better drawing a line somewhere forward of my family in the "Safe Room" IMO This gives the bad guy(s) one more obstacle they have to defeat before they can get to the rest of my family. The further forward I can make my stand (up to and including the front door) the more time my Wife may have to prepare should I not be successful.
WITHOUT Freedom of Thought, there can be no such Thing as Wisdom; and no such Thing as public Liberty, without Freedom of Speech. Silence Dogood
Does not morality imply the last clear chance? - WildAlaska -