So many complaints about how the characters are acting stupid...
There simply isn't enough information about their society and the situation to warrant such strong accusations.
There are definitely situations which exist where the Orphe family's decisions are logical.
In their medieval society, women have a much lower influence than men (think of this chapter and the women of the North).
As such, it is very important for the Orphe family to have their first born, male heir be in a position on influence.
It doesn't matter if Lamia is more competent, to save face, they NEED Uri being in a position of influence. Since he can no longer be a knight, apparently the only choice left is to become the heir. And it's not like Uri is incompetent. He's likely passable grade, which is why it's still reasonable for him to take the heir position.
Honestly, what I don't understand is if the prince is so powerful just heal Uri or something, but whatever, it'd probably be better to let this sit and allow more chapters to pile up before continuing. I can tell the maid plot point is going to be a whatever insert shoujo trope already.