This topic has come up on many forums before: how do you store a firearm for easy access when there are kids in the house? Invariably, the recommendation is to make the firearm a common fixture and take away the mystery for the kids. Allow your kids to know you have them, handle them (unloaded, of course) and ask questions. Any time they want to see them, let them (supervised, unloaded). This can go a long way to making kids less prone to seeking firearms out when adults may not be around.
Kids will be kids and the potential for disaster still exists.
If you have a pistol, maybe you can make it your primary/first-response defensive weapon and keep it in a box with quick-opening lock that reads your finger prints. If you don't own a pistol, maybe you can keep your 870 unloaded in the closet and keep the shells accessible but hidden. Learn to load it quickly.