Yes, you can, and it is more ethical to have a formal session, with all the other directors if possible, than to hold the meeting in a parking lot. However, there are some restrictions and some cautions.
Normally, there are two ways to ask a director to leave a board meeting, and both methods involve declaring a conflict of interest. If you have a conflict of interest policy (and you definitely should have one), it likely says that a director who has declared a conflict of interest shall leave the meeting, or shall leave on request of the board.
If the person does not realize they are in a conflict of interest position, another director can make a motion to declare them to be in conflict, and the board can make a decision. If the board decides there is a conflict situation, the policy can then be applied. Lacking a policy, the board can set a precedent.
I very strongly recommend that the meeting, or the portion of the meeting dealing with this individual, be held in camera, that is, board members only, or board plus legal counsel. At most, you might include the executive director but no other staff members or outsiders. The minutes should be kept separate from the regular minutes. They would only reference that an in camera session was held and that the person in question was excused.
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