Except now the family of the two year old will have standing to sue the pool for discrimination in violation of Title III of the Americans with Disabilities Act and clean up. That seems a little more real than your hypothetical lawsuit from somebody offended to be in the same county as an HIV+ person.
I don't think so.
The Americans with Disabilities Act requires reasonable accommodations, not total.
I do not think asking a person (or their guardian) who has a serious life threatening illness to provide documentation that they do not pose a risk to other patrons as an unreasonable accommodation.
The child in the pool would be in close contact with other patrons and as the pool owner stated he did not know the potential for transmittal from a 2 year puking on another patron (not unreasonable to assume a sick child might puke in a pool). I do not believe this is a strong case for violation of the American with Disabilities Act.
You missed the point, which was not technical at all. It was to shed light on the possible motivation of the owner: he did no have to believe the person was contagious; rather, he might have treated this case as the possibility to be sued for knowingly endangering the guests. An average person is likely to know about that rather than the act you mention.
Technicalities are trees, but there is also a forest, you know...
Q. Since when HIV is a disability? Do your really think that a person with tuberculosis has a right of entry everywhere under that act?