Shi ni Modori Reijou wa, Kanpeki na Shiawase wo Teniireta - Vol. 2 Ch. 3 - What I Wished for in My Seventh Life

[Simpleton]

So let me get this straight, the evil Duke's plan to get a daughter as the next Queen is:

Step 1: Get Daughter #1 happily engaged to the Crown Prince, such that unless there is outside interference, she will definitely become the Queen just like he wants.
Step 2: Send in Daughter #2 to disrupt the engagement he orchestrated in Step 1 of the plan.
Step 3: Order Daughter #1 to arrange the assassination of Daughter #2, because she is disrupting Step 1 of the plan in accordance with Step 2 of the plan. This should remove Daughter #2 while linking Daughter #1 to a crime that would have her deposed should it be revealed.
Step 4: ???
Step 5: Profit!

Dude Duke must really have hated girls in general. If we want to assume some kind of 4D or 5D chess then maybe the goal was to drive the Prince insane so the Duke can step in as Regent?