I agree with low recoil/tactical buckshot as the best choice if you've just gotta use a shotgun. BTW, in defensive use (you aren't wingshooting birds), the shotgun butt is placed on the pectoral muscle midway between the nipple & top of the shoulder, not in the shoulder pocket. If the elbow is kept down (should point at the ground) while pulling the butt in to tense the pectoral musle, the punishment is much reduced. You might also consider trading for a 20 gauge or autoloader of either gauge. The 20 may be more limited in factory ammo, but the buckshot load is sufficient for defensive use indoors.

Given your situation, I'd strongly suggest 40-45 gr .223 loads in your carbine. The FBI found them to be less penetrative of building materials than pistol ammuntion. Just make sure you run 100 or so rounds of your choice through your particular choice through your AR to ensure proper function and get the sights adjusted properly.

I'd also strongly suggest a decent pair of sound amplifying ear protectors. You want to be able to hear before, during and after firing in the house.