I know exactly what you mean about it feeling like a heavy burden to have POA. In the first couple of years I found it particularly difficult, having to make welfare and financial decisions on her behalf - I really did not want to do it, but someone had to.
It is a good sign that she has mentioned a care home, and she may be right that it could work well for her. My mother has been in a care home for 7 years now, and after a few weeks of settling in she has really loved it. You could start to look around for a care home which would take her for a few weeks respite to see how she gets on. When I chose my mother's care home I used
Guide to over 17,500 care homes, nursing homes and residential homes providing care in the UK, also the leading UK review site for care homes and nursing homes.
www.carehome.co.uk
There is a lady in my mother's care home who did actually choose to move in relatively 'early', as she had the insight that she couldn't cope and her children lived a distance away. That's really unusual but it worked out well for her.