Carcel's brother - Miguel - was engaged. His fiance (they deeply loved e/o) died. He's grieving. The imperial family seized the opportunity and "offered" an engagement with the illegitimate princess. The reason is political - they want Carcel's family to prove their loyalty to the imperial family. One way to do so is to have Miguel marry the princess. Carcel's family cannot rlly refuse bc 1) that is the imperial family and 2) they know this is political and that the emperor is basically testing them and their loyalty.

I honestly forgot what's going on and where we are. I'm totally lost