you can put food grade DE (diatomaceous earth) under the PINE shavings (not cedar) to help discourage bugs from taking up residence in your coop. but get the kind that people use for gardening NOT FOR POOLS - the pool kind is heat treated and is dangerous to your chickens. DE is not a poison, the food grade DE is not harmful unless you breath in a bunch of it (like any sort of powdered substance) so make sure if you use it that you don't put your face into the bag and take a deep breath! ha ha.
regarding the cedar issue:
i would say it depends on how much cedar gets into your pine shavings (regarding the question about your source and how much is too much). i'd be careful at any rate. cedar has oils in it that can cause breathing/lung trouble for all manner of critters.
also, and i don't know how big your coop is and thus how economical it would be, but there are different kinds of powders and sprays (chemical insecticides) made for birds and poultry to treat mites (but only use those deemed safe for birds!). you could research those and maybe use them to treat the corners/crevices etc if you feel comfortable with them.