You should not have a problem with fluoride as long as you spit it out and wash your mouth out. Otherwise, fluoride in the body causes numerous problems. Iodine is the best chelator of fluoride. You could try that with your kid.
I really think the problem you're having with Iodine is an excess of bromide. Bromide comes from many sources. If you don't want to use Iodine to try to displace it; maybe you should use the salt loading therapy daily. That will get rid of bromide too.