What about creating your own DGPS system. Place a fixed GPS near the field and a GPS on the kid. Chances are that both GPS's suffer from the same random errors because they're pretty close, so subtracting both positions could possibly remove most of the random errors and give you a fairly precise position of the kids' GPS relative to the fixed GPS. You could even use 2 or 3 fixed GPS's as reference around the field.
Meindert