Redlib, sorry to hear your mum has dementia.
I know that when my mother was diagnosed (she has Alzheimer's and no short term memory) I found that trying to understand dementia and learn about it was a really steep learning curve for me. I hadn't had much prior experience and thought it was just when you had memory problems. As I'm sure you're finding out, dementia is not just about memory problems. There are many different types of dementia and they can present differently.
There is some good general information here:
https://www.alzheimers.org.uk/info/20007/types_of_dementia/1/what_is_dementia
And lots of good information over on the Alzhiemer's Society website you may find helpful.
You likely cannot force your mother to accept her diagnosis, or even that there is anything wrong with her. Many people with dementia also have a condition called anosognosia, which means their brains are not capable of processing the information that they have an illness. They literally cannot comprehend, or understand, there is anything wrong with them. Asking someone with this kind of neurological impairment to accept that impairment, is like asking someone with a broken leg to hop down the street on that leg. It won't work; their leg is broken. Dementia can cause the reasoning part of your brain to "be broken" and no amount of logic or discussion will change that, I'm afraid. It was one of the parts of my mother's dementia that was so very difficult for me to grasp at first and it certainly caused no end of frustration for us both.
I'm really sorry that you and your sister are getting the blame. I'm afraid this is also very common in PWDs (persons with dementia); it's usually the persons doing the most caregiving and helping who get the blame for everything, and not uncommonly, a lot of abuse (verbal and even physical) as well. I know that telling you this doesn't change anything, but you're not alone.
There are, as you say, not a lot of choices. You can step back (for your own sanity) and wait for a crisis, or you can go ahead and put care in place.
If you have not sorted out Powers of Attorney (both financial and Health and Welfare), that is something to do ASAP.
Others here in the UK can offer better advice on how to get PoA and also what route to take, to access services (the Local Authority, Social Services, et cetera).
It does sound as if your mother would benefit from increased care, but that doesn't mean YOU have to be the one to supply it. Again, it depends on what is in her area, but some ideas include day care, lunch clubs, sheltered accommodation, extra sheltered accommodation, maybe some respite in a care home while you figure out options, carers coming in, hire a cleaner/gardener, sitters or befrienders, you get the idea.
I know that my mother, pre diagnosis, suffered from crippling, horrific anxiety and possibly depression. We tried all manner of medications and interventions but nothing worked. I know now, that the dementia was the real problem--that and the fact that she couldn't take her medications properly (and ended up in a mess because of that issue). What she needed to not feel anxious was 1) to be relieved of the responsibility of trying to look after herself, because she just couldn't any longer and 2) to have 24/7 companionship and supervision.
I'm not saying your mother is at that stage, just that we often hear reports of a person with dementia having bad anxiety, depression, expressions of suicidal thoughts or wanting to die, and it's often because of the dementia.
I am sorry you are feeling upset, guilty, and alienated and that you are not a "good daughter." I would point out that you are clearly a caring person who is very concerned for her mother's well being, which makes you a good person in my book. I do understand the guilt, and think all of us here on TP know about that (we call it the "Guilt Monster" and advise you poke it hard in the eye with a pointy stick). But I also want to say that you are not the bad guy, no matter what your mother says. The enemy is dementia, not you.
You might have a look in your area for support groups and carers' cafes and the like. I love TP and it has been a life saver, but my support group is also helpful and I couldn't cope without it. It can be a great resource. The Alzheimer's Society and/or Age UK may be able to point you in the right direction:
https://www.alzheimers.org.uk/info/20011/find_support_near_you#!/search
And don't hesitate to call the Alzheimer's Society and Age UK helplines for advice.
Very best wishes to you and your family.