Get another dog. I'm not saying replace the beloved one you have, but get one that will make noise. And put your gun in a gunvault (or other quickly accessed) safe.
You can "What If" yourself to death on this subject. If you hear someone knocking around the garbage cans and break a window, then you have all the time in the world to get out of bed, unlock, load magazine, rack slide, take a whiz, make some breakfast and then shoot the bad guy.
But what if you wake up to the feeling of the barrel of a gun to the back of your head? Then you've go no time to do anything, so having a loaded pistol under your pillow doesn't help either.
Bottom line is.. you have no idea how much time you'll have to "prepare" for your encounter.
You can teach your kids all you want, but kids are their own person, and they're going to do what they are going to do. I teach my kids all sorts of things and of course.. they follow exactly what I say on everything I teach them, every time. (pft).
I told my son not to run in the kitchen a million times because he'd hit his head on the counter and it would hurt. And of course he didn't stop until he actually did hit his head on the counter like I told him. I don't want him learning the same lesson with my gun.
Get a dog that barks. You get an early warning protection system, and you he'll retrieve a tennis ball.