I didn't read the whole thing, but I got this out of it. The dentist is a tool, and how he handled it was poor. Being a tool aside, he should have simply instituted a dress code, at which point she would either have adhered to it or been fired for cause.
That said, however, I am a proponent that any private business owner who has at most private investors should have the legal right to hire and fire whoever they want, whenever they want, as long as it does not break a legal contract. Likewise, all investors and customers have the legal right to decide if they shall continue to engage in business with that owner.
Once government funding is involved, it gets more complicated. Also, as a dentist, I don't know how complicated it gets because of insurance companies and such.