BHowes, I am sorry this is upsetting for you all, but glad your mother will be safe and cared for and hope the care home works out for you. I hope you will get some relief from the demands of 24 hour care, and get some sleep.
I was at a dementia carers' support group last night, and this topic came up. A lady in the group is moving her mother into a care home, and asked for advice. She and her sister have taken it in turns to stay with their mother, but they both live hours away from their mother, work full time, have their own families, and their mother now requires 24 hour care and they can't do it any longer.
Twice a month, the group is led by a neurologist who specializes in dementia care (and is the consulting neurologist at the care home where my mother lives). His advice was that if you think the person won't remember it (short term memory issues where they don't remember anything more than five minutes ago, as a rough guideline), and/or you think it will upset them, then don't tell them, as it will do no good and will possibly do harm.
So, for whatever it's worth, there's an expert's opinion.
I absolutely agree with blaming a third party, usually the doctor (or hospital if they were in hospital prior to the move). If your mother says, where am I? Why am I here? I don't need to be here, I want to go home! then you might try the approach of: Mum, I'm sorry you're upset. You are at the care home/rehab place/whatever you want to call it because the doctor says you need looking after/to get your strength back/to have your medicines sorted out/for a little while. I don't know when the doctor will say you can go home. Let me see what I can find out for you.
I'd follow that up with a distraction (food works for my mother, or a walk, or an activity). I think the key is reassurance, validating emotions, staying calm, shifting the blame off of you, and picking a party line and repeating it.
The neurologist also told us last night that a patient with no major medical issues and not much anxiety/"going home" syndrome (his term) will need at least two weeks to settle in a new place, probably longer, and those with more anxiety/going home syndrome/other issues will need at least six weeks to settle.
So don't get upset if she doesn't settle in right away. Give it time. Establish communication with the staff so you can call to see how she is doing, when you are not there (possibly better than you think, and probably better than she reports to you).
The neurologist also said, very firmly, that while it's perfectly understandable for families to feel upset when they can no longer provide hands-on or live-in care, to try not to beat yourself up for it. He said that if we had a family member who needed surgery or radiation therapy, nobody would ever expect us to operate on them or give them their therapy, so why should we expect ourselves to become dementia experts and full time caregivers? You can only do the 24 hour one-to-one care for so long, before something will give.
He reinforced that a move to a care home doesn't mean you are no longer caring for your mother, or being her carer, just that you are not doing the hands on caregiving. There is still a job to do, just in a different way, and the care home placement allows you to focus on other things.
He also said that in all his years of practice, he's never had a patient who wanted to go into a care home, but that he also never has had one, who didn't need to be there.