If these are red spider mites (don't know....check them out; maybe take some in to a nursery for ID?) You'll have to do something that will involve dismantling everything no matter what. I've read that completely spraying all the surfaces of the plants with warm soapy water will help. Then rinse the plants to get rid of the soap. You should repot the plants too, as I think the soil can have eggs and larvae. They don't "feed" on animals luckily, but if they crawl on your cham it could be very annoying.