Get yourselves some matching T-shirts that read:
Chlorine: Breakfast of Champions!
I realize this does not help you with your problem! I recall using some anti-chlorine brand shampoos and such, but not sure they really helped me.
You might try using a very heavy duty, and pleasantly scented, moisturizer all over your body. The constant water is very drying, and I wonder if you let your dry skin really suck up a bunch of good-smelling moisture, if that would help throughout the day? Maybe even just some plain old almond oil.
Just a guess. Good luck!
"The best rides are the ones where you bite off much more than you can chew, and live through it." ~ Doug Bradbury