I will definitely teach the kids about guns but at 2yrs and 4yrs they just cant be trusted.
We never found this to be the case. Then again, I started with them handling their own, real firearms, as soon as they could hold them. Both were shooting thier .22's at 4, and had "shot" a bazilion rounds in dry fire, on the living room floor, before their first live round.
I always felt safer with my kids with a loaded gun in their hands, than I did many of the adults we were often around and shooting with.
As far as the lock boxes, dont bet on the kids not getting into them. I didnt use that type of security, as the only loaded weapons in our house, were what I was wearing, and a shotgun in an electric car rack that was mounted by the front door. The switch on that, was separate from the gun and hidden, and would have taken both kids to activate and remove the gun, which never happened. When they were older, and could reach it, I showed them how it worked, and they told me they never did know where the switch was.
My youngest son was always fascinated with locks, from a very young age. I saw him methodically go through combinations on the small "locker" type locks, until they were open, and it usually didnt take him to long. He also had picking standard locks with picks down pat before he was 8. If kids are determined, figure they will get it done.
The main thing is to get them on board as early as possible, explain things openly, and constantly allow them to handle and shoot them. Worked great for us, and we never had a lick of trouble.