I am in Canada and our LTC system is different. Do you have a local Alzheimer's Society that you can contact for assistance? The only other thing I can suggest is make use of the Internet and research what assistance is available to you.
Kudos to you both for what you are doing! I know it's hard (I look after both my parents by myself).
A suggestion I would make if you don't mind. And I know you have education and experience already, so if what I say is what you are already doing, forgive me.
Educate your teenagers on Dementia so they understand why Grandma says and does the things she does. It is a very important learning opportunity for them, and a teaching opportunity for you on how to help someone with dementia. Let's face it, the chances of us having some form of it is there. You can prepare your kids for how to handle it and how you wish to be treated should it ever happen to you. Depending on their ages, they may also be a means of help and support for your Mom as well.

I know it's not good to move AZ patients too much but have her admitted to a geriatric psych unit to adjust her medications. This helped my Dad a lot, they completely changed his meds and is now able to stay at his assisted living facility for now. If she can't go home after the admission the hospital will be able to get her into a LTC facility at discharge. The LTC can not deny you a bed based on your insurance. Medicare does not pay for LTC for dementia or AZ though which is crazy.

If she gets admitted to the hospital for anything, she would be able to get admitted to a nursing facility much faster and easier. I know this for a fact from working at a hospital and working with the case managers who helped families get their loved ones placed somewhere.

Other than the Alzheimer's, she is healthy as a horse. We have her diabetes under control. She has been to the ER for a fall, but never admitted.