I am thinking this is adaptation of a novel. But this adaptation has only reach the first part of novel...
and the summary, maybe it is for novel. after all it is not fit between the summary, and title with the story plot.
And yeah, the two guys is her first cousin. But, from what I remember based on background (historical drama), in that time usually they accept the first cousin marriage as long as they are not in the same clan (marriage inside the same clan is forbidden). So, even if Miaoke with the Yi (the prince) is possible, it is not possible with Lin Chen, as they are from the same clan.