Hello and thank you for contacting us. This is Dwayne B. and I’m an expert here and looking forward to helping you today.
Generally, a COA or HOA can do anything that their rules and regulations and by-laws allow them to do so long as the rules and regs and by-laws are passed according to the process set up in them (ex. a vote by a certain % of members).
In your case there is a problem that is immediately apparent. The language they are complaining of ""Each Residential Unit shall be used for residential purposes only, and no trade or business of any kind may be conducted in or from a Residential Unit or any part of the Condominium...the terms ”business” and “trade,” as used in this provision, shall be construed to have their ordinary, generally accepted meanings, and shall include, without limitation, any occupation, work, or activity undertaken..." doesn't seem to have a good definition. Normally that language, which originated in city ordinances, is used to restrict residential property from being turned into commercial property but is not used to prevent rentals.
So your first argument would be that the definition is unconstitutionally vague. In addition, there is a rule sometimes known as the "Scrivener's Rule" that came from England and essentially it states that if a term in a contract is subject to two meanings then the court is bound to accept the meaning offered by the party to the contract who did not draft it (or have it drafted) so long as that meaning is reasonable. This applies even if the definition offered by the other party is "more" reasonable.
I don't see there being a huge issue with someone being fined for listing their property on the AirBnB website. It's a little unusual, but generally a HOA/COA can make anything prohibited that they choose to make prohibited, again assuming that they followed the proper procedure.
While you can ask for the hearing, you would be better off hiring a lawyer to represent you in this hearing and then, if you lose this hearing, in the lawsuit which would follow. The concepts and principles involved in this case are much more complicated than they might appear and include issues of Constitutional Law (including grandfathering or ex post facto) and the power of the COA/HOA.
You can sue for your attorney's fees as well as any other damages you have, but the COA/HOA will have a lawyer involved for them, even if he is acting "behind the scenes" and so you should as well.
If you choose not to hire a lawyer then you need to do a lot of research on the issue I set out here as well as familiarizing yourself with the Rules of Civil Procedure, the Rules of Civil Evidence, and then do a lot of legal research on the issues we've discussed because you're going to have to "educate" the judge on the law on this matter.
If your question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a Positive Rating so I receive credit for my work. Of course, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered.