ok theory time. I think the uncle/general/duke of the crown prince killed his sister, the second queen, in an attempt to get closer to the thrown and position his nephew as the crown prince. And due to the princes young age and obvious trauma and continued abuse by the uncle, he would be a good "puppet" for him to control.
I also think that the princess is lying about "killing her brother". I think she knew that the author was in closet and is not only using that as a ploy to get more information on the enemy and extend the due date for the secret message, but to also test the author's allegiance and see how far she'd go to keep the first prince safe.
And yes there is probably some discrimination among nobility due to the princess's gender, however, with how strong they portrayed the first queen and her family, i believe that she would've taught her daughter the pride that can come with being a queen/princess and the true power that can come from not just from sitting on the throne but also from standing behind it. Which helps support her strong history of doing all she can to help support her brother's dukedom and reputation, goin as far to hire a fan fic writer. Yes she want more power for the espelianos and control of the crown, but she doesn't want to be wholly in charge of it.