Perhaps if your museum has an attorney or financial adviser who is of counsel to your organization, you could talk with him/her about your dilemma and get some sound advice on what to do.   There are usually pretty clear governance and fiduciary responsibilities -- including directors' and officers' liability if the organization is not run properly or the board makes egregious errors in judgment -- to consider with any 501(c)3 organization.  So perhaps there are some ways to restructure the board or its executive committee so that authority is spread out more, or so that others on the board are compelled (by their own self-interest/protection) to take action about this problem.  Sometimes people will trust or accept a recommendation from an attorney (delivered kindly and mildly as prudent legal/business advice), when they'd absolutely reject the suggestion if it came from a mere executive director or administrator.  Good luck in this difficult situation.    

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