It's a mind control game - you do not have to murder someone to prevent them from doing harm ;) If you expected to be able to murder Maven and have Kana be okay with it then you haven't been paying attention to Kana!
Well, her mother tried to kill her family and *tortured* her to literally thoughs that MC is another dream of her dying brain. I understand that she want to keep mother away from her family by herself but still strange. That stance against sun in kill-route made me to replay hour of gameplay. Glad she at least punched her mother in a face for all shit.