CHEs are no more dangerous to animals and children than a bulb is; both can cause burns if touched when on. So, for safety don't let your children any where near the enclosures without your supervision, and have you considered getting cage locks for your tanks so that your children can't accidently open them?
CHEs produce heat but not light, as John explained, so therefore you can keep the temperatures constant without having a light on, disturbing your WDs photoperiod. They do get very hot and should be ideally controlled by a thermostat meaning that the temperatures will stay constant and accurate. Your vet's advice sounds good; with a sick reptile temperatures need to be kept warm and constant and the environment needs to be quiet and calming, so keeping it a kid-free zone will probably be the best idea while Lee makes his recovery.
If you can't get a Ceramic Heat Emitter right away or would prefer to continue using a bulb then you could also consider the use of a Under Tank Heater (under-tank heater/heat mat) - I don't like using these inside lizards' tanks as there is a risk of burns, but used underneath, outside the tank, or, if the tank is wooden, you could use it inside the tank but mounted to the side, to provide a background heat at night making sure the temps don't drop too low.
Sounds like Lee is about to make his trip home, or has done already.? I hope he makes a quick recovery and gives you something to smile about knowing how well you have done for him.
