So i'm at work and bored and thought this was neat so I did this is a VERY VERY ruff MS PAINT sketch
Ok so what you would do is build a panel into the table that the controller sits on/in. This panel is held on by hinges. When the game isn't being played you would have a panel that fits over top the hole so as to inclose it without any one (daughter) being able to see it/touch it. When you are ready to play, you would open one of the side doors and simply just push the controller up through the now open panel and it would fit into place like that. As for the cord, you could build a removable plug panel at the bottom so that when your ready to play you just remove the plug and plug in the cord to the PS2.