@aiebime But everyone (but Yeon) knows read hair = royal family.
And her dad and brother would even know his face.
Let's not forget that the prince was waiting for father&bro after they left the king, then we skipped back in time to Yeon&the prince's lunch. So... this means, after Yeon left, the prince had gone to father&bro. Probably because of the feast? Or to tell them he'd make Yeon crown princess? Or just to mess with them in general. Hopefully, we'll know (at least the beginning of the conversation) next chapter.