I honestly do not see the point in writing a complaint letter to the person you are complaining about. Pointing out "hey, I don't think you did your job in this situation. In fact, I think you did a horrible job in this case, and here's why" is not likely to go anywhere but in te circular file. Instead, I think that if this is something you feel strongly about and believe that the AD needs to work on the way she handles these situations, I suggest you write the letter to her boss. If you want to keep everything out on the table, you can cc: her. Still, her boss can make sure her process is reviewed and ensure that she's following organizational policy.