Red mites are not going to be eradicated by just washing I'm afraid. They wedge themselves into the tiniest nooks and crannies and will resist even concerted efforts to scrub them out!
If you have red mite, I would recommend soaking your coop in one of the many chemical solutions available as your frontline defence then back it up with a heavy and thorough dusting of Diatomaceous Earth once the house is dry.
The mites don't live on the bird, they live in the house and come out at night to feed but if you treat your birds with something like Ivermectin spot-on, this will also help at night when the beasties come out, until you have got rid of the problem.
If you take one of your birds off their perch at night and give them a good ruffle up over a sheet of white paper, you will see if you have red mite as they will drop off and show up against the white. You can also use a torch to see if you can see them crawling along the perches, looking for their 'sitting supper'.
If red mite are left untreated, not only will they put your birds off roosting, thereby maybe exposing them to predator issues because they are not in the house, but the red mite will find the birds, even on top of the house and over time, will begin to deplete their energy levels and can leave them aneamic at best and dead at worst.....broodies are particularly vulnerable due to the length of time they spend in the house, making them an all day breakfast!
