I would second key00's remarks on not using an enclosed case. make a room in your house off limits for your child and put an open rig of some sort in there. These pump out 70C+ air, and in a confined space you'll never get them mining (ie they'll overheat and shut down before you submit any hashes that matter). If you have a garage or a drill, just build
http://www.bitcointrading.com/forum/mining-hardware/guide-make-your-own-open-frame-rig/ out of wood. costs maybe $10, and all parts can be found at any hardware store.
I also wouldn't 'dangle' the cards, they need to be secured to something... Since you're interested in litecoin/dogecoin go to
www.reddit.com/r/dogemining and follow one of their beginner guides.
Of course. This is why manufacturers like Dell, HP, etc all run their enterprise class servers in open air rigs. Also it's why all datacenters have really big empty spaces with milk crates stacked on top of each other running 10Kw on a 19" x 30" foot-print in a milk crate.