I'm genuinely lost as to what is happening. Is the sister hallucinating something?
Basically, she wanted her sister to have a normal life, a beautiful life.
Sister instead went insane, became a killing machine, lost all her memories from trauma and all that.
Little sis wants to put her out of her misery because she believes that her older sister shouldn't suffer anymore. She's hoping that her sister will die an assassin so that the original her won't have to die remembering that pain. So now she's getting super pissed off and worried because she thinks it's shifting from a fight to kill "Shue" to a fight against her sister.
tldr Little sis wants to mercy kill Yuki because she perceives her as having a constant cycle of suffering
Something like that. At least what I got.