Hi, not sure about the fly zapper thing, I've never heard of one being used before but maybe you could get your children interested in bugs and teach them that we are in their environment?
I would get some bug cathchers, nets and books (I think Usbourne do a Little Spotters book of insects etc)and use it as a way to educate and have fun with your children. We do a lot of things like this at school and it's amazing how many children who were previously scared become the keenest bug explorers and don't react to things flying round them.
A cup and strong piece of card is also a great way of catching bugs and releasing them safely back out into the night.
I know I haven't really answered your question about the bug zapper (I'm afaraid I'm a bit of a bug lover!) but hope this helps.
Can't advise on the bug zapper thing, but why don't you zip up the tent inner long before dusk to keep the bugs out of the bedroom. I hate having thing buzzing around me at night, so I can sympathise with your children.
You can zip up the main part of the tent too, but I know it is much harder to keep it closed up with children popping in and out all the time.
Electric bug zappers work well but you need to close the flaps, to stop new bugs coming in, unless leaving it on overnight - the UV light actually attracts them.
I always hang one under the parasol when camping in the South of France. You can then enjoy your wine whilst listening to frying mosquitoes
I understand what your saying firefly, about catching them and releasing them, but when you have a load of midges or mozzis in teh tent because one of the kids left the door open, its not really possible to be kind.
I think you sometimes have to accept that bugs will come in through the open doors. However I always used to keep the mesh zipped up on the bedroom after waking one morning to find we were sharing with a huge thing! More tricky now with the 'van.