I have just gone through a mite episode so can relate.
You are best to identify the type of mites you have as it will determine how to proceed with cleaning the coop (more below)
I had Northern Fowl mites and used both Permethrin spray (before it turned cold) and then sulphur powder. Both treatments are known to be effective. With the sulphur I dusted the birds around the vent, under wings, on the back and chest (keep the dust away from the head) weekly for three weeks AND mixed it into the dust baths. Previously I sprayed with Permethrin on a day 1, 5, 14 cycle; I still had mites and switched to the sulphur powder because of cold temperatures. I am pretty certain both will work BUT persistence is required it is not a once and done process. Permethrin dust can replace sulphur but I did not have access to it at the time.
I have read that mites and other such critters will attack weaker birds and not appear on others that are in good health. Notwithstanding you need to treat all birds once you have an infestation.
You also need to deal with cleaning your coop. NFM live on the host almost permanently (can live off the host for up to 3-4 weeks) whereas Red/Poultry mites live in cracks and crevices mostly around the roost areas (MUCH harder to get rid of) and come onto the birds at night to feed. In my case I cleared all bedding out of the coop and moved it to the run (if you have red mites burn it). I then sprayed/soaked the entire coop (walls, floors, roof, roosts, nests, feeders, etc); did this weekly for 3 weeks.
I now inspect all birds weekly or so.