I absolutely hate red mites. After two years on the trot with bad infestations we eventually moved to plastic coops - ruddy expensive but they're really been worth it. Having said that, we did still get a small infestation in one, but a quick spray woth poultry shield and it was much easier to clean.
With our wooden sheds what we did was this:
Moved the shed to somwhere away from where your chickens normally live - we put it on the drive. I then stripped it down into its smallest components - if that's possible. I sprayed everywhere I could with Poultry Shield - left it to dry overnight. Next day did the same again, left it to dry overnight. I then brushed Diatomaceous Earth into every nook and cranny - paying special attention to the actual perches. It was like rubbing flour into a rolling pin, get it right into the ends. For me that has been the way to go with wood.
Every clean out the floor and nest box gets a sprinkling of DE, every few months the chooks get it powdered all over them - we look like big grey eedjits once we've done them all - the entire household is red mite free then! DE has been the saving grace for red mites and lice - forget the lice sprays and expensive chemicals. Two good dousings of DE on a chook with lice, once a week for a fortnight, has cured ours of them. We also sprinkle it in their favourite dust baths during the summer. Only real downside is that some of our Light Sussex tend to look grubbier than they could look - but they're also a darned sight happier
You can't stop red mite - wild birds bring them in, they always come back. Off the bird they can live for 6-8 months, so if it's possible, moving your chooks to another site helps.
Ah - one other thing we've done is to make a perch and attach it to the coop floor with long bolts/screws, so that only the screws are touching any coop wood - the ends of the perch are free-standing. This way any red mite has to crawl up the bolts. We then cover the bolts with vaseline or something else sticky that you can wash off - this way the red mites get stuck in the vaseline, and never get to your precious chooks - giving them a well-earned sleep