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I have great sympathy for the letter writer, but little practical advice. This situation totally sucks. Do NOT let your sister or anyone else guilt you into taking care of your mother (and I am relatively "pro-guilt" in other situations). Your mother is GONE and it's nobody's fault. Your life matters too! Be patient with your sister, but she is wrong. Perhaps your sister does not realize that schizophrenia is a true disease, with a biochemical basis (the evidence for schizophrenia is much stronger than for other mental health issues that are labeled as "diseases"). Maybe if you gently educate your sister about your mother's grim prognosis she will eventually come around.
Your poor father, too. This may sound harsh, but if I become schizophrenic and refuse to take meds, I HOPE my wife and kids abandon me. Because I love them and want them to be happy, instead of stuck in hell.