This is so hard for you. I looked after my parents from the UK and them living abroad 800 miles away, for over 15 years, and it was so hard, in so so many ways. I even gave up my job due to this, and finally moved over to be there for them- but too late.
But one thing I can say is that you have to respect her wish to not go into a home- and find a way, privately or with the help os social services, or a mixture of both (as we did in the end) - to provide a support structure for her, which allows her the independence she wants. You are lucky that the UK, despite massive cuts- has much much better support structures for the elderly than most countries. Could you take a few days off to visit her GP for advice with her, and talk to social services, but also neighbours who may have local experience and know good and trustworthy people who do private care too. I feel for you as it takes its toll, physically and emotionally x