How can I explain to my Mom that she needs to go into a nursing home?

I'm my mother's only child and the only family member who lives anywhere near her. Without getting into the backstory, we haven't exactly had a great relationship. Suffice to say that my childhood was abusive and I left home when I was 17. I still tried to include her in my and my children's lives to no avail. She only reached out to me, her siblings or friends when she needed something and eventually alienated everyone despite our attempts to contact or visit her. It's been a couple of years since we were in regular contact but I made sure the management company of the senior building where she lives had my phone number in case of an emergency.

A few months ago, the office contacted me because she was being a nuisance... knocking on neighbor's doors in the middle of the night, screaming and yelling and calling the police a few times a week, convinced that the super was stealing from her or moving things around in her apartment. She also burned a plastic container on her stove and had been taken in for an overnight psych evaluation. At the time, she was found competent and allowed to return home. Despite our past, she's still my mother and needed help so I started visiting and calling frequently. Eventually I learned that not only was she not eating well or taking her meds even though I'd bring/buy her food and remind her to take her meds but her behavior had become even more erratic than the management company led me to believe. She would cover the sprinklers in her apartment with plastic bags because she swore that they were cameras that the super was using to spy on her. No matter how many times I'd remove the bags and explain that the sprinklers were for her safety, she'd have them back up the next time I visited. She was also leaving the building at all hours of the night (in not the safest of neighborhoods) and would sometimes be brought home by the police because she'd become confused. A couple of weeks ago, she was threatened with eviction if her behavior continued because it violated terms of her lease.

I was looking into assisted living (there's no room for her in my apartment) and had set up an appointment to take her to mental health clinic for an evaluation when she had an extremely bad episode of paranoia and was admitted to the hospital. She was diagnosed with dementia and it was decided by everyone who's evaluated her (even the bioethics department) that it's no longer safe for her to return to her apartment alone. There are no resources to hire help for 24 hours so she'll be going to a nursing home.

She's been in the hospital almost 2 weeks now and feels there's nothing wrong with her so she should go home. Her extreme paranoia is being controlled somewhat with medication but she gets very agitated and verbal. My visits with her start off nicely then she lashes out and calls me all sorts of nasty names, accusing me of wanting to get rid of her so I can have her money (she has some savings but not enough to pay for more than a month of home care). She'll be discharged to a nursing home soon. I researched and visited several places and let the social worker know my top choices which are all very nice, well rated and reviewed and have specialized care and activities for patients with dementia. They're also close enough for me to visit weekly if not a couple of times a week.

So how do I explain it to her when she's convinced there's nothing wrong with her? Can I even explain it to her in a way that she'll comprehend? Or should I expect to be nothing more than "the bitch" as she's now referring to me regardless of what I say?