Being a pyromaniac, I go for the blow torch/weed wand approach if the hens have only the one coop. You have to get into every last corner, between any slats etc, and repeat that regularly all season. Ideally, have two henhouses so you can treat one with fire then creosote. Check really well at the ends of perches.
I also treat the hens themselves - it's said that red mites don't stay on the birds during the day, but of course some do, or they wouldn't be able to travel around or re-infect the henhouse after treatment, which of course they can do.
Having just reread your OP I see you are talking of a broody coop. A sitting hen will be so uncomfortable if there are red mites in her coop, plus the chicks will not do well either. You will still have to treat the main henhouse, as well as the coop, as they will be there too.