lol. Let me guess. At some point it's going to be revealed that the third princess was simply told he was dead, because the king and nobles sent him on that mission so he would die. And they convinced her he was dead after some time, and even though she had been in love, she bought it. Her smack-talking him is a bait by the author, she's just doing it to look good to her new beau.
She will eventually join Warrena's countryside harem around chapter 50 or something after somehow finding out he's alive. This is why the author made her the third princess - because someone that far from the throne (and a woman no less) has almost zero royal obligations or duties and the royal family can do without them, no narrative reason for there to be a major conflict if she abandons the royal palace. Even if she doesn't join the harem there will be some story elements involving her somehow.
Still a lazy setup, but not as lazy as just saying "you were cheated on, now go live in the countryside, loser" (granted there are manga out there guilty of much worse setups).
Can't think of many other reasons why the author would bother flashing to a scene with her and giving her a name and face that we're likely supposed to remember - it's like he's setting up a slow B-plot. Granted he didn't spend much time on her design and made her look villainous. Her smack-talking the MC in such an obvious way seems pointless, so my theory is that it's a bait and she's pulling some courtly intrigue scheme of her own. Of course, he could have just been adding some stuff that wasn't in the novel and her presence in the manga is literally meaningless.