this question has 2 possible correct answers. #1- what ever you can grab quickly. #2- whatever you can hit your target with. i would think the latter would be the most important factor.
Change your tactics, not your weapons, GO TO YOUR KID first.
If for some eason you can't do this, add layers of security to buy you time like a dog, door alarm, motion alarm, dead bolts and of course secure windows. Any gun and any load can penetrate dry wall and hollow doors.
You also will never know for sure where your kids are. They may get up to take a ****, watch TV or play with toys so good habits now will work for life as your family grows.
Go to your kids.
With your kids behind you, what loads do you want in your gun? For me, indoors it is Buck in the gun and slugs in the saddle. I happen to use #4 buck because I live in a dense population area and #4 is very good for use outdoors in tight spaces. When I am rural, #4 is for dogs and coyotes only.