... The law trumps the desires of the owner of a private business serving the public.
The biggest battle in Florida has involved "private" clubs, even ones like the American Legion, etc. They thought they were exempt, not being open to the public. Wrong. They have been stomped on, too. No smoking inside. ...
We went through this in the UK.
[Ignoring cinemas, malls and the like because they've been non-smoking for years at the wishes of the owners.] First it was supposed to be restaurants then they added bars that sell food. Then the antis were afraid that this would lead to confusion so they pushed for all bars except private clubs. Then the antis were afraid that bars would convert to private clubs so they were added too. In the end it's now all indoor public places and we, along with Ireland, enjoy the most draconian smoking laws in Europe, possibly the world (except maybe California!)
The only exemptions AFAIK are prisons and, yes, the bars inside the houses of parliament. Disgusting.