Welcome to TFP!
Where do you maintain your chlorine level? We normally recommend 4ppm free chlorine with 20ppm CYA as a buffer for best results, but dogs being dogs, you will have them drinking the water. So that may not be the best idea, though we probably can't give you good advice on the dog health issues.
To answer your question, yes, a UV system may benefit you and help control CC. Many residential UV systems are marketed with overstated claims, so it's well worth some research to be sure you get a system that has enough power to be worth the effort and expense to install it.