I'm really confused about what Mikado knows. His reaction on how Shinomiya's family tells us that he somehow knows that Shinomiya and the president are in some form of relationship. But then he's surprised that he has a girlfriend?
>Not just killing the girl
She has an older twin to replace her anyway, the family will probably forget her in a couple of days, no harm done. Might even be relieved because of her terrible personality.