The sister really is narcissistic and not as smart as I was hoping she'd be. First of all, EVERYONE wants/wants their daughter to be Empress. Removing your sister as an option won't bring you ant closer to the throne.
Second, you are still a concubine's daughter. If your sister falls it is going to screw you over as well as that will affect the reputation of your whole family, and I don't see you making plans to fix that. Third, and most importantly, the Emperor already made it clear he didn't like you by making fun of your appearance. Just do as Elsa did and let it go.