If any mold spots clean with 10% chlorine solution which kills mildew on contact.

you should have a sweet chlorine smell. sounds like it's working just fine.

The likely cause is too much chlorine or other chemicals fom the water treatment plant. 

If you have a choice, get the chlorinated version; the non-chlorinated version doesn't work as well.  

If they get sick because they forgot to change a filter or maintain a chlorinator then that's their issue.  

You will want to make sure you have it fenced, with the proper type of gate latchthat is child proof, have all signs in place pointing out swim at your own risk, nolifeguard on duty, a lifesaver ring, etc.Regarding expense, many people don't understand how logical it is to switch fromchlorine to salt system to keep the water properly chlorinated.  

A quick attempted fix would be chlorine tablets in the lines to see if it clears it up, which it may. 

If you look at all the specialized products, they all contain a halogen derivative to kill mold - look at a periodice table of the elements and the second column from the right contains all the "-ine" compounds, chlorine, fluorine, astatine, etc.

Could it be the chlorine in my water or maybe its just asbestos I breath in as I rip up old flooring?

For really difficult problems, we typically attack the issue with Chlorine Dioxide, a non reactive, ultra strong oxidizer.