Options for dealing with an abusive elder?

My grandmother has alway been physically and verbally abusive towards me. After a fall a few years ago, and with limited mobility, she has lashed out more towards my mother and I. FYI, my mother takes care of her – takes her for her check ups, bathes her, feeds her, takes her out. She recently had a hip surgery, and after returning to our home (nobody else will take her in, so we have no choice), she began calling extended family and making allegations that she is not fed or cared for so that they will visit her. She also claims she is unable to walk most of the time so that she will have to be attended to, however, when alone, she walks just fine around her room. Worse yet, yesterday, in front of my mother and I, she called my aunt to claim that we had abandoned her in front of my aunt's house. Then, she walked out of the house (pushing her wheelchair; YES she walks fine!!!), set it on the roadside (YES on the road itself!!!), and then when a man came to help her, she told him that we had abandoned her there and had him push her to my aunt's place which is 10 minutes away. He even made a police report. As my aunt's family has cut ties with her, they refused to let her into the house, so we had to pick her up and talk to the man to have him tell the police they need not come by. When I brought her home, she tells my mother that she spoke to the police and told them about her; after my mother called her out on that lie, she threw a tantrum. And no, she is not suffering from any mental illness and is completely lucid!!! She has always behaved like this, but now, somehow, it's worse!!! After this incident, my mother and I are afraid of the extent she will go to for attention, especially since such incidents are escalating and it gets worse when she doesn't get the reaction she wants! Especially more so now that she knows that most of the family does not wish to speak to her. I'm truly afraid of what she will do, as she has always taken it out on me if she can't get what she wants. We are trying to find a home for her, but cannot afford most places and are afraid she will not be accepted in the cheaper community homes because of how she speaks to others (she always tries to humiliate people or behave as their superior; she is very domineering and needs control) and her tendency for violent outbursts. We are at a loss as to what to do, as having her remain with us is a danger to our family! I need help, please.