Does Medicare or Medicaid pay for home care?

My mother has been in a rehab facility for 2 weeks and she is insisting that she go home. She has been homebound for about 4 years with myself and her sweet neighbor doing all her errands, shopping, taking her to DR Appts and house cleaning. She landed in the rehab center after not eating, drinking or taking her meds for almost a week. She got very ill and dehydrated. She went to see her primary care doctor and he sent her straight to the hospital to be treated for the dehydration. But he told her before she left his office that she was in such bad health that he thought she needed to go to a nursing home to live. After 2 days in the hospital she showed her butt really bad. She ripped out her IV in front of a very young nurse who was terrified at her behavior! My mother is very mean and will do whatever it takes to get her way. She will show her butt and throw a tantrum as she did that day. When my mother told me that story about terrifying the young nurse and how blood was squirting all over the floor, she was laughing and she had the greatest look of joy on her face...She is a terrorist and gets off on causing others pain. The nurse called me shortly after it happened and I could still hear the tremble in her voice. She said the doctor was releasing her, which was unbelievable to me because she was in such bad shape. They wanted her out of there because she was being so violent. I said to the nurse that I couldn't believe that the doctor would release her in such bad shape, to go home alone. That is when the nurse told me that mother had lied and said that she didn't live alone, that she lived with her neighbor. She had called the neighbor to come pick her up but the neighbor refused. She told me that she was washing her hands of my mother, that she couldn't handle her anymore. My mother is a sociopath and has been very abusive to everyone in her life. Especially me because I have been the only one stupid enough to keep coming back around her. A friend told me once that I have "Beaten dog syndrome". He said no matter how much she beats you down, you are still right there for her whenever she needs you. Which is BTW the ONLY time my mother calls me...when she needs something or when something is wrong...She never asks how I am or how her granddaughter is because she could care less. But I have always came running to rescue her, not because she deserves it because she had been terrible to me, but because there is something deep inside of me that feels the need to take care of her.,,the need for her approval. I just always try to be hopeful that if I do enough for her or pay her bills or buy her whatever it is that she needs that maybe she will change, that maybe she will love me one day. All to no avail unfortunately. She looks a me and speaks to me as if she hate me...She does hate me and that is very hard to deal with. She told me once that she wished she had gotten an abortion. That's pretty damaging to hear let me tell you. She has no one left but me and there is no way that I can take her out of that rehab center and care for her on a daily basis. She is too damaging to my soul. I simply can not take the emotional, verbal and mental abuse that she dishes out to me when I am anywhere near her. Not to mention that I live an hour away from her with a family and child of my own to take care of. My husband travels a lot for his company and that leaves all of the child care and the care of our home up to me.
I was told that Medicare would not pay for home care and I just don't know what to do at this point. Any advise would be greatly appreciated,