Regarding the matter of succession to the throne, the crown prince (princess in this case) is normally the oldest son (daughter in this comic) of the Empress (Emperor in this case, lol since the genders are reversed). It's all about the status of both their parents. The second princess is the child of the previous Emperor which gives her legitimacy over the others.
Now, if the second princess were to die or be removed from the succession then the first princess would be the logical choice since the third princess' father was the Empress favorite... but he was just another concubine, not the Emperor.
Edit: Oops, posted this in the wrong chapter. Sorry, but anyway I'll just leave this here.