Mornin' all!
Yes, kids (and adults) die in accidents with guns... as well as with household chemicals, bathtubs, power tools... the list goes on. People with guns and kids (or other people) in their house should do all they can to minimize the chance of anyone "accidentally" discharging a firearm. Keep it locked up, the ammo in a different location, and be sure that EVERYONE in the house is trained, or at the very least put through an age appropriate gun safety lesson. Again, education is key. Accidents will and do happen; and I'd love to see the statistics of those accidental gun deaths in the context of how many of the victims had been educated about gun safety.
"Country kids" are taught about guns from before they are physically able to use one, generally the accidents we hear about are suburban kids who're likely to have never held a real gun or been out hunting. I'd be interested in the related statistics along that vein.
I don't even own a gun right now (won't until my kid is old enough and physically able to fire one, and is properly trained to do so), but when I do, it's unlikely I'll be buying one for hunting. If I have one, it'll be one of the mankiller variety, because other than the pleasure of target practice, it'll have one use: protection. I'm not ashamed to admit that, nor should I have to be. It's what handguns are made for -- stopping an enemy; defined as "anyone threatening my life, liberty or property." I'm ready and willing to comply with the laws that allow me to do so. I have no argument with most of the laws currently on the books.
The debate will continue to rage on, I suppose.

I don't mind at all, since it means at least SOME Americans are giving a damn enough to educate themselves; if for no other reason than to argue!!!