I'd agree with Jag. Seek information, seek assistance - and talk about it. Not to god, or to yourself - those CAN be good to get things straight in your head - but to someone else physically there, who can sympathise and give advice.
The biggest help for me came when social services and the NHS finally did the Healthcare Assessment, and then recommended the right home for her needs. Before that, it was all down to me to find somewhere, and I simply didn't have the tools. I could look at homes, and probably get a fair idea, but without knowing all the info on medication and care and the practicalities of her 24 hour needs, I likely wouldn't get the best fit.
How do I cope? By knowing that I've managed to get her into the best home in the area for her needs, where she is looked after and safe and happy in the moment. And to be honest, having done that, to try to put it all out of my mind as much as possible. "I've done all I can do, I can do no more", to paraphrase popeye. Making sure that I go out and do stuff that I enjoy, not feeling guilty.
An update for those who have been following. Last week was the yearly "renewal assessment" for the continuing funding, where we go through continenence, psychological state, medication, behaviour, etc. Sitting around a table in the care home for an hour were the NHS assessor, the care home manager, me, and my mum, talking in great detail about how bad her behaviour could be, and how ill she was. In that hour, I don't think she once registered that she was the one being talked about. And not once did she recognise who I was.
And that, bizarrely, is the think that has made it easiest. Previously, although she was mostly gone, there were still bits there - she knew she knew me, but not where from. Now the last bit of my mum has gone, which actually makes it a whole lot easier to visit, because there are no more tears and unhappiness when its time to go.