Driftwood and similar materials have lots of crevices for eggs. Toss the wood in a container with about 10 percent bleach and scrub it up. Same with the cage if its wood. Hot sun rays will bake the wood, the bleach will break down to salt after a while. Treating the iguana is a different story.. a good long warm bath will help.. but you have to scrub him up the mites will stick in pouches in the scales, under sheds, anal vent arm pits etc.
Basically its all out war with those red bastards. :) they can come back if you overlook a spot.