A rather odd chain of events led to me getting a commercial pesticide applicator's license with certification to treat animals.
There's really only one thing to remember: READ AND FOLLOW THE darn DIRECTIONS!
Some formulations of Sevin are labeled for use directly on chickens. Carbaryl is some mean stuff though, and I try to start with something safer before moving to the big guns. See what the label says on your spray (I'd guess permethrin, resmethrin, or something that ends -ethrin)?
DE is processed in several different ways, make sure you're not using something processed for swimming pool filters. Once again, best to get something with a label that says it's for use on poultry.
Also, carry the mite fight beyond the chicks. Remove all the shavings/bedding, clean out the coop, puff some dust into the cracks and crevices where mites will hide out, and treat the new bedding with DE or a dust.
And now that you're having some success getting rid of the mites you have, figure out where the mites came from, and take steps to make sure they don't come back!