My wife came up with what I think is a brilliant idea to keep the kids mozzie and fly free...
Use an old dome tent (minus fly) as a play / refuge area. They can be put up in a minute or two - you don't even really need pegs because they are self supporting and, without the fly, the tent's mesh 'inner' doesn't tend to get blown around much.
They are also completely insect proof (and free if you have an old dome tent at home).