I would personally (carefully and wear a mask) shake a thin layer over the floor- like shaking carpet powder.
BUT I would put it in greater amounts wherever they take a dust bath in the coop, if they do.
I also put DE right on my chickens periodically. This needs to be done for it to be a preventative IMO because I have had mites pop up with just putting it on the pine shavings in copious quantities.
If you can get them to put it on themselves via a dust bath, all the better.
This is just my opinion. I hope others tell their experiences.
I have a wood floor and use sweet PDZ and DE interchangeably for the floor every other day or so, so that I use the whole floor like a poop board. It is very dusty but works well for me. It won't work in a cold climate due to frozen poo on the floor.
I would LOVE to try sand on the floor.
Good for you!
Don't neglect your walls if you have crevices where the red mite can hide. Those should be sprayed with Poultry Protector or Orange Guard (or something of the sort) to keep them away---
or if you like chemicals, permethrin spray periodically to get those mites killed if they are there.