Ronsalk, hello and welcome to Talking Point.
I've not read all the responses, so apologies if I repeat something.
In my opinion, this will likely not achieve the result you want. You state that you want your mother to understand she needs help.
If your mother has dementia, then you, in all probability, cannot get her to understand she needs help. The logic and reasoning part of her brain no longer functions correctly and no amount of proof, reasoning, or discussion will change that. To be blunt, her brain is broken. Just as you would not expect a person with a broken leg to be able to walk on it, you cannot expect a person with dementia (PWD) to be able to function in a logical and reasonable manner.
Does she sometimes have clarity and understanding? Quite possibly. She may also sound very lucid, or actually have a lucid moment when her memory and understanding are okay. But higher functioning reasoning is usually very impaired.
Of course, everyone with dementia is different, and presents differently, and different types of dementia damage the brain differently.
However, many people with dementia do not have the ability (again, due to the damage to their brains) to understand there is anything wrong with them, so they will deny they have a problem, in the face of overwhelming evidence to the contrary. This is called anosognosia.
You might find a different approach brings the results you want: Mum, I know you don't want to go to this other doctor, but your GP said you needed to go, so we will just go and get it over with. I know there's nothing wrong with you, and you know there's nothing wrong with you, so not to worry. I know you don't want to go; however, the GP/NHS says you have to.
Always blame things on someone else, a figure of authority is a good choice. I blame the doctor for a lot of things! (I know you don't like taking so much medicine, Mum, but the doctor says you have to. I know you hate the compression stockings/TEDS hose/JOBST stockings, Mum, but the doctor wants you to wear them. Et cetera.)
The UK Alzheimer's website has lots of good information about dementia. This might get you started:
https://www.alzheimers.org.uk/site/scripts/documents.php?categoryID=200120
Wishing you all the best.