I know it's small comfort, but lice are actually easier to get rid of than mites. Lice don't hide in the cracks and crevices of your coop so the most you'll have to do (besides dusting each bird) is clean out the coop, put in fresh litter, and sprinkle some of the permethrin in the litter, nesting boxes, and dust bath areas of their run. And, thankfully, you and your children aren't at risk of lice infestation from the chickens.
Just make sure to re-dust your birds within 10 days and replace the litter again. Usually two treatments are adequate, but to be sure you have everything killed, recheck you birds about 7 days later for any live bugs. BTW - those egg (nit) clusters on the feathers will remain until the feathers are lost during molt. They are not a sign that the permethrin didn't work and your birds still have lice.