Dan,
If you have a concern about having a loaded handgun in the house with children, then may I suggest that during the time that they are awake, that you keep the handgun on your person in an inside the waist band holster.
At night time, when all are asleep in bed, you can then keep the loaded handgun in the nightstand or somewhere closeby for home defense in case of an intruder.
Either way, the handgun is under your control, the children have no access to it during the daytime because it is on your person, nor at night time when they are in bed sleeping.
If the children are up and about at night time when they are supposed to be in bed, then you may have to make other arrangements at that time.