yeah, but doing the right thing to the letter will hurt both sisters right now. The empress invites unnecessary competition when the throne was her birthright, and exposes her pregnant and vulnerable sister to the machinations of the nobles, people who owned her, abused her etc who will try to use her to get the throne. She's giving her a title, rank and land. And elevating her to the highest position she can without having her be a competitor for the throne.
I know. But it's still sad
Well in the first place, Lynn's mom has a problem too. She was accepted by the emperor and will be given by a title but she ran away before the emperor could talk to her. So, throughout the years the birth of Lynn was hidden from public so everyone assumed that the Empress is the only wife. So, it could stir a problem if Lynn identity was revealed especially to the relatives of the former Empress.
Idk but hiding her identity is kinda insulting imo... you wanna protect your dad's reputation (he still cheated) by hiding your sister's identity... nah...