I'll stick to addressing your Rem 870.
That is the gun we used in LE. The way I taught it to be carried, cocked, on safe, with an empty chamber and the mag loaded. It takes a split second to get it into battery.
If the gun is cocked, you can't work the action unless you hit the mag release. Small kids as you mentioned aren't gonna figure this out.
It takes a tad be of training to get the gun in battery, you just practice grabbing your gun hitting the mag release (or lock) working the action as you release the safety.
Heck this is the same procedure I used when I use to do a lot of duck/goose hunting. I never hunt with a round in the chamber (regardless what I'm hunting). Its quick enough to get the gun in action. If it works for flushing birds it will work for bandits.
Again small kids wont figure this out. What you do have to worry about with kids and Cops (they are a lot alike) is them dropping something down the barrel. I've inspected a lot of police shotguns over the years, I've found pencils, cigarette butts, wads of paper, and everything you can imagine poked down the barrel.
Put some electrical tape over the barrel, it wont slow down the shot going out but it will slow down things going in. You wouldn't believe how a pencil will jam a pump shotgun.