I hope your example is hypothetical because having a gun for protection isn't going to be effective either unless you give each kid a gun.

In cases like Elizabeth Smart the problem was a lack of threat awareness and prevention—open window, no alarm system or not on turned on because windows are open, hiring people to do odd jobs.

In case of fire a family should have working smoke detectors, an escape plan that is practiced every six months when the batteries in the alarms are changed. Upper floor bedrooms should be equipped with throw-down chain escape ladders and the kids should practice using them if old enough. If not old enough they should be sleeping near the parents or an older sibling who is assigned, per the plan to get the kid. Mom gets Susie, Dad gets Jr., everyone meets at the curb in front of the house.

The plan would be similar in case of the intrusion alarm going off except they retreat to the safe haven room. If family is on different floors create a safe haven room on each floor the occupants can go to and lock down and have some means to communicate with each other.

There a lot of possible solutions that do not involve wandering around the house with a pistol.

hardening each of their doors and locking them at night as with a safe haven.

What is your plan in the case of a fire with kids on three floors. Have the been drilled to escape and congregate at one spot. Has the plan been practiced? A

How is having a gun in your bedroom going

In cases like Elizabeth Smart the window in the kid's room was open and accessible from ground

a plan similar should have in the case of a fire you practice with the kids so you aren't running around trying to find one.