Miranda is not a true psychopath...spoilers
If she were, she would not have been traumatized by the rape, so traumatized that she was unable to become a surgical nurse (the trauma manifested physically, causing her hand to shake). Also, her tolerance for frustration seemed to have decreased; the girl at the dry cleaners had always been a *beep* but Miranda didn't erupt at her until after the rape. While Miranda did exhibit sociopathic tendencies, the way she responded to the rape was quite normal.
I think she did care about her dad, as much as anyone with her wiring could. When he fell off the porch swing, she ran to him with urgency and didn't roll her eyes like someone acting out of a sense of duty might have. Further, people who have sociopathic tendencies possess a remarkable ability to compartmentalize, which is why she could maintain a relationship with her father without informing him that she let her mom die and able to comfort her dad after she killed his dog.
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