I would not use DE on hermit crabs. It would be toxic to them because it would dry out their gills.
I can speak from experience about the mites though. To get rid of them you should bath the crabs in declorinated water a couple of times a day. Be sure and put them in the water upside down and then flip them after a few seconds if they don't do it themselves so that water gets all the way into the shell to wash it out. Be sure the bath is shallow enough that the crabs can stand up if they want though. Move them to a dry area and let them move about to drain their shells.
To get the mites out of the tank you have to either toss or boil everything in there and then scrub the tank well, paying close attention to the seam areas then rinse it and leave it to dry in the sun. I would also be sure and clean the area the tank was in really well to make sure there are no stray mites. Check your houseplants if you have any nearby.
Set the habitat all back up from scratch. Once you are rid of the mites only offer dry foods like the hermit crab pellets or meal sold in pet stores for awhile because the mites seem attracted to the wet foods. Be sure to change the water bowls daily, clean the tank weekly and bath the crabs often and you should be rid of those annoying bugs for good!
