@SussexDave: I too thought I could never contemplate a care home for my mum until she no longer had any awareness. However, there came a time when, despite being articulate and mobile, she suddenly stopped recognising her own home and could not be left alone for even a minute, as being alone anywhere, no matter how familiar or secure, was the same to her as being totally abandoned in a strange place. That would mean I couldn't even go to the loo, put the kettle on, or put washing in the machine without her shouting out in distress or coming to find me.
In addition, she had started wandering (I think to gain some context to where she was, as she had no memory of the area or the house from the inside) and would leave the front door wide open. She had to be brought home by police one night, while under a paranoid delusion that there was an intruder in the house holding me hostage and other lurid things. She would always be most active, indeed manic at night, obsessively looking for things, making phone calls if I wasn't there (or sometimes if I was), or bursting in on me in the night because she had either forgotten I was in the room or wanted reassurance I was still there. Time had no meaning for her, so there were no boundaries of appropriate behaviour for different times of day - long-term sleep deprivation can be a huge problem for the carer.
If we went out, I could barely run to a shop within sight of her or even get a ticket at the parking machine without her wandering off or getting anxious. Going to the supermarket for an hour became impossible without a neighbour to watch her in my absence.
It came to the point where mum was not safe to be on her own at all and I knew I could not cope alone 24/7. Social services had been encouraging me to find a care place for some time, but I had stalled because I dreaded having to do it, knowing that in her right mind it was something mum would have abhorred. However, when she became at daily risk of harm and my own health and sanity were at rock bottom, I knew I had to face it. I was hugely apprehensive that she was too cognisant to accept it and had no idea how (or whether) to explain it to her.
In the event, I took the advice of the staff and social worker and played it as low key as possible, initially pretending that we were just going to have a look at this place and go for a cup of tea etc. The strain of having to play it covertly was terrible, but she did in fact accept it better than I had hoped. As per other threads here, it seems it will never be possible to be entirely open or truthful with her about where she is now and that it is permanent; but she is physically a lot better (eating regularly, not at risk of wandering, getting a proper sleep routine, daily activities, on site medical care), and most importantly has 24-hour company and supervision from a variety of specially trained people, which I would never have been able to provide on my own.
Before your relative goes into care, it is impossible to imagine they will ever accept it. And while they may never do so in a reasoned way, it is possible that they may not be as traumatised as you think, and it will be the best option in the long term (if you can find a suitable place with the right staff and facilities).
I would also say that while toiletting issues may not currently be a problem, they can occur without warning and encompass not just continence, but obsessive "parcelling" and other ritual behaviours. My mum was previously the most fastidious person and only had mild "accidents" through dementia while at home; but in the last few months (she's now 85, going on 86), she has started to display some of these behaviours and I have to admit I'm tremendously relieved not to have to deal with them myself in a domestic setting.
So I would say please take your time to think this through and do look thoroughly at care homes before making the move yourself. It is a huge strain being a carer 24/7 and if your mum does ultimately need residential care and you have also been through the upheaval, both practical and financial of giving up your own home and social life (the support of old friends can be vital in such circumstances), you may regret it in the long term.