Another tactic to use alongside cleaning and spraying etc is to add Red Stop to their drinking water. This is an organic product which doesn't affect the eggs but makes the hens' blood taste nasty to the mites so they can't feed and eventually starve themselves out of existence. You add the Red Stop every day for the first week or so and then less often when the problem is under control. Dosages are very low, so although a small bottle may seem expensive it lasts a long time.
If you keep the birds in a closed run with a roof, where wild birds have no access, you're much less likely to get redmite as it arrives on the feathers of wild birds, which shake it off when they preen, or when they land in an open run to feed or drink from the chickens' utensils. Also, whilst overhanging trees give welcome shade to a run, you may get redmite drifting down from the feathers of wild birds perching or roosting there. So the problem keeps recurring, however often you clean the coop, and a new coop won't make a difference except at first before numbers build up again. Mites can also be imported accidentally on wood chips made from trees where birds have been roosting, so this sort of wood chip is best avoided as it also goes mouldy and releases spores which are dangerous to both chickens and humans
Whet sort of coop do you have? Plastic coops have far fewer nooks and crannies where mites can hide, and come apart for complete cleaning. The worst type if wooden ones have felt roofs, where the mites creep between the layers and are totally inaccessible. However, if taking any coop apart, be aware that mites may fall off onto the run floor and just crawl back up once you're finished cleaning it. Some people stand the coop legs in pots of water, or even paraffin, to prevent this, though I suppose the ramp is still a way in for mites.
However, I think the main thing us to prevent access by wild birds in the first place, as not only do they bring in mites but also the risk of viruses and bacteria. If the run is large enough (min. of 2 sq. metres of floor space per bird) the chickens are perfectly happy in there and are safer from predators as well. My girls have lived happy, healthy, mite-free lives for 7 years now, in their big covered run, and I know they're safe and not at risk from mites or larger predators.