CalOptimais a public health care agency in Orange County California that administers health care services for Orange County residents on Medi-Cal. If your sister has MediCal through CalOptima, she should be able to get any kind of medical care she needs for free, or for a very low copayment. The only requirement is that she receives her care from a doctor or other provider who participates in CalOptima Medi-Cal. She can get the same care through CalOptima as she could through Medicare -- and pay less for it; the only advantage she'd get with Medicare is that she'd have a wider selection of doctors or other providers.
Your sister could become eligible for Medicare, too, if she qualifies for Social Security disability benefits. (By the way, Medicare is not related to SSI, which is a supplemental income program; it also has nothing to do with your father's tax return.) Your sister's disability check may be coming from the state or county, or from Social Security, depending on what program she's qualified for. If your sister is not receiving Social Security disability benefits, she may be eligible for them if she worked for even a short time before becoming disabled. She can apply for them at any local Social Security office. If she qualifies for Social Security disability benefits, she will receive a monthly benefit payment, and when she has been receiving Social Security disability benefits for 24 months, she becomes eligible for all parts of Medicare.
Regarding your concerns about how your sister is being treated by your other sister, if you feel that she is not getting the care she needs, or is not receiving all the benefits she might be entitled to, you can contact the county office of Adult Protective Services in Orange County, where your sister lives. It is their job to investigate the well-being of people with disabilities and others who are vulnerable to abuse.