You'll need to treat the mites. There isn't much available here in NZ (I've tried Smite which was useless and don't get me started on diatomaceous earth) and there's very little you can get at a physical shop.
I found neem oil worked well to treat the coop and you could make it up into a spray to do the chickens/chicks with (make sure it's pure neem with no added pesticides). I mixed up half neem, half warm water and painted the inside of the coop. I only had to do that once, whereas with other products you have to keep treating weekly until you've broken the life cycle. Neem stops them at all stages. The coop is the main one to concentrate on as mites hide away during the day in cracks and crevices and under bedding and come out of hiding at night to feast on your birds, though broodies provide a 24/7 buffet. For the birds I'd make up a 5-10% solution to spray on them.
Vetafarm also do a spray (you can buy it as a concentrate as well) thats called Avian Insect Liquidator. I've only ever bought it online. It's an Australian product that is the permethrin with a couple of other active ingredients that make it more effective, giving up to 6 weeks protection. It's safe to spray on finch chicks so safe for chicken chicks. The only time you wouldn't use it is if you are intending to eventually eat the bird/s you are spraying.
Infestations can be caused by wild birds or rodents getting into the coop. Do wear insect repellent when you clean out the coop as I got bitten by the mites pretty bad and had a very itchy Christmas. Also shower straight after and wash your clothes in hot water to prevent transferring any mites inside. Strip off in the shower, stick your clothes in a plastic bag, add some fly spray to the bag and wash them as soon as you've showered.
They are not nice to deal with so you have my sympathies.