About the issue with .223s, to use one in a house would be nothing short of insane. For outdoor home defense (say if you have some property out in the country), it's probably a bit better-suited, but you still run the risk of shooting your neighbor's cows. This is not a concern for my uncle who lives on a big ranch that is densely populated with very thick pine trees. He uses an AR-15 A2. God those are fun. Unfortunately that does not make them well-suited to urban home defense. Let me reiterate: that would be insane.
There are ways to at least try and prepare for the contingency of a hostage situation, and that is to get everyone in the same room and guard the door with that shotgun and don't let anything through. That only applies if you realize there is an intruder before a hostage situation ensues... I don't know how to advise you in such an instance. Your aim must be absolutely dead-on or the unthinkable will happen. I think the best way is to avoid such a situation ever occuring, and achieve some means to alert you to an intruder the moment they get in the door, cram your family into a room that has only one way in and out, get them huddled in a corner with no windows, and blast at anything that moves while you stand at the only doorway there is.