I've thought about this before, but why are readers so adverse to characters getting redemption? It's not like the 2nd prince was an irredeemable trash, he simply believed what his brother has said.
And is it not a good thing if he wakes up from this idiocy and changes for the better?
Adding in my own two cents here, there's also a fatigue about people being offered redemption
while they're still 100% asshole, and, moderately predictably, they don't take it. Or "redemptions" that involve the people staying shitty (the most complained about example being "Sometimes I Wish You Were Dead", which, among (many) complaints people have about it, ends with a "happy ending" the ML definitely does not deserve, having given non-apology after non-apology, after some extremely shitty behaviour)
Honestly, the "upright to the point of blindness/stick-up-their-ass" characters usually have better ones than usual when it pans out, and it does pan out more often than not (usually with an
actual apology for their behaviour up til now), so it's not so much "redemption arc" at this early point, as "He screwed up once, and is likely to course correct quickly precisely
because he's a justice-type."
The slow life remains out of reach. Although at least her parents support the
idea?