I need to get live-in help for mom, in exchange for rent or reduced rent. Any advice on how to go about this?

Mom has severe dementia. I am her 24/7 caregiver. She needs help getting into and out of bed, is mostly incontinent, resists taking showers, is a fall hazard and hard to get her up when she does fall, and can be very contrary and stubborn, at times resisting anything I try to do for her or ask her to do. She was recently in hospital for uti and low grade pneumonia. Is now in a rehab facility. I want her to be able to come home, but I will need help now, as my back was starting to hurt before she went into the hospital, and I don't think I can go back to the constant physical and emotional demands without any help. Her health insurance only provides in-home care (a nurse comes out and takes her vitals, a physical therapist comes and gets her to exercise her legs for about 30 minutes, and a nurses aid comes and tries to get her to take a shower, sometimes successfully) several times a week for only a few weeks. We cannot afford any in-home care beyond that. I am thinking of offering room and board to an individual or couple, for reduced or no rent in exchange for help with mom. Maybe a nursing student? I would need someone who understands dementia and who mom would respond well to. Mostly I need someone who can help me get her into and out of bed, who can help me get her up if she falls, and who can watch her, (including assisting her when she walks around and helping her with toileting/diaper change) for a few hours several times a week so I can go run errands or (gasp! spend time with friends, you know, do some things for myself, like they always say we should), run errands occasionally, and can occasionally keep her occupied while I am home so I can get some things done at home without constant interruption. My biggest concern is getting someone who would look good initially but turn out to be dishonest or, even worse, abusive.

Mom will most likely be discharged within a week, and while in the rehab facility they keep calling me to ask me to come in and stay with her because she constantly tries to get out of bed during the night and during the day when she is not in physical / occupational therapy or being fed, she won't stay in her wheelchair for more than a few minutes before trying to stand up and she is not steady enough to stand or walk alone, and they are not allowed to put a seat belt on her in the chair, or railings on the bed, and they have to take care of the other patients too and can't watch her every second. So, what I thought might be a short time of respite for me (visiting her, but having some time at home to catch up on some rest and get things done that are hard to do with her home) has not turned out to be much better than when I had her here and took care of her myself, and does not give me much time for looking for the person or couple I need to help. It is hard to get started on anything because at any moment the rehab place might call me and tell me they need me to come in.

Oh, also, the rehab place is saying that If I can't come in and watch her when she is restless and needs constant attention, I need to "hire a sitter" to come in and watch her. That would have to be 24/7 because you can't predict when she will be contented and when she will be restless. At least they finally started giving her a sleeping pill last night so she finally slept thru the night, but she will still need someone during the day. If I could afford to "hire a sitter" full time for the days, I would take her home and hire someone to do it at home, but I can't afford it!

Any suggestions would be greatly appreciated!