one of the beauties of Iodine is that it is a daily need. if the chlorine pool was every day, you would negate your supplementation over a period of time. in this case, you can let your kids swim with confidence knowing that they will continue to be supplemented but not continue the chlorine soaks.
if you wish to give them an extra drop after swimming, that would be ok, but not worth causing dissent or hard feelings with your loved ones.
have fun and enjoy your family. that is what good health is for and it the most healthy thing you can do in this instance.