> They do not have their shower working so I wash as soon as I get home
I'm not sure about colour loss but it does seem a shame that your dog has to get wet twice. Less of a problem in warm weather but not so much fun when it's cold. How long before they get their shower fixed? Presumably you could delay treatment for a week or two til it's ready, or ask them to supply some other alternative such as a hose or bucket. Not ideal, but better than the alternative of leaving the chlorine in the coat, getting partially dry and then having to wash again at home.
I guess you need to balance the benefits of treatment with the problems caused by the broken shower but it would be a shame to stop going all together if it's helping your boy.
My chap has been swimming in the river today and it does him the world of good - he smells and feels scrumptious, and has conked out for the afternoon! Sorry not a terribly helpful observation :)