There's no proof that they are related at all till the end of novel.
Shulli's late husband married her cause yah she looks a lot like the late empress and shulli's late husband, the emperor, and the father of ML all fell in love with the late empress but she chose the emperor.
That's why when Shulli's late husband died many thought that is marrying Shulli act of getting back at them.
That's why Emperor and ML's father adores Shulli.
Not at all sweetie, because if we took account their family tree( family tree of the late empress and shuli) they came from a really different type of nobility. It was clearly explained in the beginning. ( 1-20 chp? Not sure... Maybe. As i remember shuli's family history was clearly stated and for that you can say that they are not related at all).
i'm confused. so shuli is the crown princes mother?