In 2-3 player Citadels, can the unique district abilities be triggered twice?
Yes you can use the unique ability twice.

The rules here state the following regarding 2-3 player games.


  each player has two turns each
  round (one turn for each character). 


So if a card says it can be used 'once per turn' then you will get to activate once during the turn of each character you took.  

The rules make a distinction between 'round' (The process from character selection and calling each character in order) and 'turn' (when a character takes and action and/or builds a district and uses special abilities.