A chamber of commerce is normally a 501(c)(6) nonprofit membership corporation that gets the leadership the members elect.  If it is a corporation, it has to have a board of directors (or some group functioning as a governing body even if it has a different name).  In many states, it must have a minimum of three directors.

I can understand your frustration in dealing with directors who don’t want to be there and you can certainly suggest that they step aside.  But if what you really want is to be left alone to do your jobs, it might be more fruitful to try to tell the board how much more you could do if they supported you and left you alone, rather than trying to impose their pet projects on you and giving you help that isn’t help and that you don’t need.  Or you might be able to get a clear understanding of what you and the current executive director do on your own and what their other appointees do on their own.

If a direct approach doesn’t work, you might talk with some sympathetic and respected members of the chamber who could help press your case and perhaps even run for the board and assist. You might lose your jobs, of course, if you go outside the current board for help.  But you have to decide how much hinderance you can take before the job becomes intolerable.  You are not required to work for a group that doesn’t respect what you do.