Yup, it's a serious problem in the large wooden coops that seem popular here. They're great until some mites move in. Most are almost impossible to clean properly as you're finding out. Nobody I know in the UK or in Catalonia builds these types of coops.
Don't put DE in a broody coop!
If you are sure you have red mites then that's a coop problem, not a bird problem. A sever red mite problem takes many treatments to sort out. Some keepers find it is easier in the long run to burn the coop and start again. Of course, a lot depends on the size and...
What sort of mited are they?
What bedding are you using in the broody coop?
Are the broody hens getting off the nest and outside to bathe, poop and eat?