Dear Josh,
Thanks for your reply. Agreed if the "daily" meant Calendar day, then 3x14 would indeed be $42, but the signage and the ticket itself said nothing about their definition of day. It was $4/hr and $14/daily MAX.
Maybe I was naive, and I have been so in the past.
The hotel parking attendant told me personally "$20 a day" so that was my source.
Regardless, the manager has ignored my requests and I am going to dispute all but $28 of the charges with American Express. They are a reasonable company to do business with IMHO and they allow disputes if you can justify the complaint, which I think I can.