"Child-proof" storage for Minecraft multiplayer?

Solution 1:

Best way to do this would be to create an ender chest, this chest is separate for each player, meaning only you can see the items that you have placed inside.

Although, this does mean that your kid could put items in the chest that you wouldn't be able to see, so just make sure that you put all of your rare items into the chest.

wiki page: http://minecraft.gamepedia.com/Ender_Chest

Solution 2:

That's the only reason why hidden storage contraptions are made.

For instance this tutorial.

redstone torch is used to power the sticky piston which then moves the block over the chest. this reveals the chest. you can access the chest. When you want to hide it again, simply break the redstone torch.

just make sure that you open the secret chest when no one is near by you.