@gennoson the one thing i like this manga, the one thing i feels ita shown nicely here and very rarely anywhere else is the reason for romance.
In both cases, the reason as to why they like her are shown and explained very well. Yulan likes her because she was the first to accept and reassure him, she gave him a strong and supportive front even while she was suffering too. Thats why yulan likes her.
In the prince case, its also shown very clearly, this manga is one of the few where 'fate' doesnt seems to force things, and the prince had a very solid memtal image and opinion about her, mildly annoying at best. But she gave him a reason to shatter that mindset, after the tea thingy, he overheard what she said about justice, quite the profound line--if you ask me--and that made him think about himself, what he had done, who he is, and what that means. After the seed of doubt came and some self reflection, he realized his mistake and apologized, but was ignored, that caused a little spark of curiosity and guilt, thats what made him thnik so much about her and eventually, like her.
So thats about the now, but the other relationship is the one from the first round, that one is also explained and given reason, and so, as the reason didnt exists the second time, the relationship also didnt exists.