You should be receiving lots of help. Mum should be claiming Attendance Allowance (special Fast Track is possible) and Fast Track Continuing Healthcare, applied for by your GP. It sounds like mum NEEDS to go into a nursing home where there is a team of nursing staff to care for her 24/7. She can come home to you if well enough, you can go and see her whenever you want, but the physical care is done by someone else. My mum was too frail to live at home any more. When still at home she would reach for her jobs list as I walked in, jobs "saved specially" for me when I was newly widowed, newly disabled, with a son who had severe learning difficulties to care for, a national club to run, and 30 tons of vintage lorry spares to sort and sell. (No, that is not any exaggeration at all!!!!)
It is sad that mum is dying, but you have to think about what she needs, because it's not what any of you would really want.
Are you getting any hospice or District Nurse Support? Do you know how much longer mum has? Have you Googled "Signs of Dying" so you are prepared for how things will be in the final weeks? Have you and your sister talked about funeral arrangements, service, music etc.?
I know it's all horrible, horrible, horrible, but it's so much easier to arrange in advance, to accept what will happen, organise what you can, before it is forced upon you by circumstance. Once you are confident everything has been thought about, then you can concentrate on making the most of all the time you have left with mum. If you need to know what others here did, just ask and we will share our own experiences,in the hope that it might make things easier for you.