Briala's path in that quest is just weak.
It makes sense if Celene defeats Gaspard because she knows of his betrayal, has troops positioned and can just expose him to the nobles gathered, winning their support.
It makes sense if Briala is defeated because her power base is the elves and the Inquisition takes them away.
It makes sense if Gaspard become the sole ruler because Celene is dead.
But it makes no sense for Briala to permanently hold power over Gaspard. What, five years down the line she will threaten him with revealing that at a conclave, he had troops there and was going to break the truce? Would anyone actually care enough? If Gaspard gathered the nobles and reveal he was being blackmailed, although it would severely weaken his claim on the throne, wouldn't the nobles and solders place much more importance on the fact the Empire was being manipulated, worse by an elf, than on something that happened years ago at a ball?