My gun comes with me.
And usually my flashlight too.
I do agree that it is a good idea to have a few guns placed in strategic locations about the house, but I think they should be in spots known only to yourself and those who you deem responsible, and out of reach or accidental discovery by children.
My relative's house was broken into while she was asleep about a year ago, and the thieves went through the kitchen drawers and started on the living room before they noticed that someone was sleeping in the house and bolted. So any guns should be in unusual locations, places not likely to be stumbled upon.
Guns are popular targets for crooks, I would not put them in the same room with children. Let the thief target your basement or den or someplace else in search of loot.
If he's in your kids' room, then engaging him will be complicated as he will have human shields or hostages readily available and the likelihood of accidentally injuring one of your family members, be it by over-penetration, or simply the deafening and trauma of seeing you kill someone in front of them, will be much increased.
So my opinion is, don't give him any reason to be near your kids! Put your valuables in a location where no-one will be at night, and any sound from that area is cause for investigation. If you do have a gun in your kids' room, it should be secret from them and located where they cannot accidentally stumble upon it. Don't rely on them telling you if they do, kids like secrets. They also like to share secrets with their friends. Who like to share them too.