How do I help my mother become independent of my sister?

I have an elderly mother in another state that can no longer drive, manage her finances or cook. A sister lives with her, and has always lived with her. The sister is near 50 and our mother is 87. My mother has always taken care of all of the housing needs, living arrangements, etc, while my sister has worked. She has never contributed to the financial expenditures at home. For most the recent years, she has been unemployed, verbally abusive at times and a financial drain. The inability to drive is a recent event, though she has had to when there was no food in the house. I am helping with the finances, calling her every day and am her legal representative in all legal matters. I am trying to what she wishes, which is to try to maintain a relationship between her and my sister, as long as her well being is protected. I have been advised to look for alternative housing for my mother. Her income is about $2,000 a month, and I may be able to supplement that with about $80,000 to $100,000 in savings and equity. I would probably set my sister up in a situation and fund it for three months, to give a chance to get on her feet. A number of social workers have suggested this, including Adult Protective Services. My mother has great health care coverage, my concern is in Southern California, what should I be looking for? I can afford to help some, and perhaps I can get other members of the family to contribute some, the main issues are affordability, quality, and hopefully some continuity of care.