Assuming that the school is not a charter school or other organization that is subject to an open meetings law, board members have the right to caucus among themselves and discuss corporate business.  It is a matter of state law and the bylaws whether they have the right to call a special meeting and remove the woman as a director.  She should check the applicable provisions.

I personally believe that bylaws ought to provide that a majority of the board has the right to remove another board member, with or without cause, after notice and a right to be heard.  (See Ready Reference Page: “Bylaws Function as ‘Constitution’ of Nonprofit Corporations”) Just because they have the right, however, does not mean they ought to exercise it without a serious discussion with the person in question before taking action.  I view the provision primarily as a tool to talk to people about improving their performance, not a means for arbitrary retaliatory action. Arbitrary action will make it harder to recruit good board members in the future.