Comment by Shoto on I Was Born as the Second Daughter - Chapter 4

@Shoto I'm currently hypothesizing -and it's based as much on imagination as on the thin clues given- that the mother was the empress, and her older daughter was poisoned or deliberately infected by someone who wanted the child out of the way for some reason, maybe as a way to attack the mother. When the older daughter died and the mother realized she was pregnant, she faked her death and fled. For some reason she feared the emperor would not support her; the rival may have been conniving to create misunderstandings between them and make them suspicious of each other.

By the time the emperor sorted things out and cleaned things up, he was far behind the trail.