DE is, actually, effective against some species of mites. I've used it successfully for well over a decade in that particular way. Mind you, there are many species of mites out there, and while perhaps there are some resistant species, it hurts not to try and actually find out for your case.
I had this same problem recently. Never had any mites at current location, until my hen had been sitting for just shy of 2 weeks. I carefully placed DE all around her inside the crate she nested in, and the next morning when I brought her food I held it a few steps from her eggs, so I could sprinkle DE powder over them too while she stood. I also carefully lifted the crate, keeping it level, just long enough to sprinkle DE all over underneath it. It will not hurt the chicks or the adults.
The other thing I did to help keep and drive them out was to mix Cedar Oil - only a couple of drops - into an ounce of water contained within a little fine-mist spray bottle, shaking it vigorously right before use. I sprayed this all around the floor and the outside of the crate I had her in, on top of it and with a paper towel wiped some of the solution along the walls and ceiling of her crate, leaving them nowhere to run to between the DE and cedar oil coverage.
The mites all died and never returned.
Pyrethrum-based things will indeed work, but I personally don't use them because of the fact that the way they work is by being neurotoxic. Fish and invertebrates have the intense, deadly sensitivities to it, but I question if it doesn't have far lesser effects on the birds, so I don't use it any more, personally. As somebody living with neurological issues, its something I consider not worth risking with another living being in my care.
