To clarify the analytical evaluation presented in this answer, I will introduce a summary of the main points, followed by my answer, to show that you can help by respecting your parents' intelligence; you present no indication of age-related mental decline.
You appear to believe, based on your mother's denial of the moon-landing in 1969, that your parents do not have the mental skills to evaluate information. However, you do not indicate that your parents have been diagnosed with Alzheimer's or dementia, or that they present symptoms of such. You list your father's lack of medical background as a reason not to trust his ability to understand what he reads on Google. But, as evidenced in the telling of your story, you do not have any medical background yourself. This raises the question as to why you doubt his father's understanding of the situation. It is your father who lives with your mother; you live far away in Canada and admit to having only patchy information.
You believes that Dad is not taking Mom's illness seriously, yet according to the story Dad is obsessed with understanding it, spending twelve hours a day Googling it. If he were not taking it seriously, he would not be doing this. That is human nature and we are all familiar with it.
As an adult son living in a faraway country with only patchy information, you ask, "What can I do?" You clearly do not trust your parents' ability to think clearly, but you provide no evidence that they are not thinking clearly. A solid piece of evidence regarding your own mentality and method of handling life is the way you handled the incident of the moon-landing in this present conversation.
OP and Moon-Landing Incident As evidenced in my answer, after reading my answer you changed your account without informing me. Consequently, my answer appeared to subsequent readers like a misinterpretation of your account (see the comments and other answers), by all appearances proving your claims that people of your parents' age lacked mental skills to correctly evaluate information.
To me, this speaks of a lack of respect for the intelligence of others, especially people your parents' age. You fail to consider that many people are mentally competent into old age, meaning into their mid-nineties and beyond if they live that long. Mid-sixties is not old age.
My dear friend, one thing is obvious and that is that you don't trust your parents to make the right decision. Another thing that stands out bright and clear like the noonday sun is your reluctance to let your mother go if she wants to. But before we take this any further, let me tell a bit about myself. At the university I took the undergraduate program for clinical social work and in grad school I took a number of additional courses in family counselling. In addition, I am the age of your parents and have laid to rest both my parents and all four of my grandparents, many aunts and uncles, and some cousins and friends of my own generation. What follows is based on my professional training and personal experience.
Something puzzles me. I'm not sure why you bring up the moon landing of 1969 and use it to question your parents' ability to evaluate information.
I worry more generally about their information evaluation skills -
they are both intelligent people, but a couple of years ago when
myself and my wife were round for dinner, my mother said to us "You
don't think the moon landings really happened, did you?" - to be very
clear, she does not think they really happened, even though she was
alive to see it when they did. That kind of thing makes me doubt
whether they can accurately evaluate (or maybe whether they trust?)
The important thing is that your parents understand the gravity of your mother's illness and I have no reason to doubt that, given what you report in your story.
My answer as follows is built on the premise of professional ethics, that is, medical personnel is responsible to respect the wishes expressed by the patient and caregivers. In this case, according to your story, your father appears to be the caregiver. Because of your repeated concerns regarding the mental competence of your parents, I will address these questions and concerns. You also express emotional frustration that your parents do not comply with your and your brothers' insights and urging to move forward quickly with treatment. All this appears to be based on the belief that Mom has not decided to let nature take its course. All I have is the story as you tell it, plus my own experience and expertise in the field.
If she's decided she doesn't want to fight it, as an informed choice,
then that's fine, but it doesn't feel like that's the case and she
certainly hasn't said as much.
Yes, I think she has said so very clearly but as her children you are unable to hear it. It is normal for you and your brothers to want your mother to be well and alive many more years. Mid-sixties is not old these days. I myself plan to live for twenty or thirty more years at least, but I'm healthy and feel good. On the other hand, your mother is feeling so tired, not eating or sleeping well. She knows the only way back to any semblance of good health is through very invasive and prolonged medical procedures.
my Mother has an intense fear of any kind of medical procedure
We need to respect this. Now is not the time for her to battle her phobias; if she was going to overcome them, she would have done so long ago. As an older mother, she is very familiar with the cycle of life and death, having brought children into the world and most likely buried both her parents and possibly also her in-laws. She is obviously more frightened of the necessary medical procedures than the natural procedures of terminal illness.
I see a clash of values between adult children and their parents:
I and my brothers have tried to tell her and my father that she really
needs to be moving forward with things, to start treatment,
This is your very serious reluctance to let her go shining through. It's normal. You're only 35 and expected to have your parents many more years.
but she claims that she doesn't feel any worse than she did a couple
of weeks ago.
That statement is a clear indication to me that she is aware that she is not well and that she is content with this knowledge. However, she also knows very well that her sons disagree strongly with her wishes. Saying she doesn't feel any worse is her way of trying to put you off, getting you to back off and let her be. Why doesn't she just come right out and say that she knows she's dying and wants her children to let her be? Is it because she knows the severe resistance her sons would put up?
she says that they could drain it but it's an exhausting process and
she can't cope with it.
She can't be clearer than this that she doesn't want to do it.
I've done some very basic research and found that this kind of fluid
retention is normally treated with diuretics, which my brother and now
myself have mentioned
My brothers have tried talking to her and to my father but they don't
seem to have gotten anywhere.
...I worry that every day of delay makes my mother's prognosis worse.
This fear of losing your mother is normal. Her prognosis is getting worse and she knows it. She is fine with it, at least resigned to it. It must be difficult to know her children are adamant to keep her alive, with or without her consent. I have read of people who knew they were dying but they could not speak to their families about it; when finally they could speak openly, they felt so relieved and at peace.
A big issue for you is your father's ability to make informed decisions and evaluate your mother's care based on his age and on his background. However, you say:
I've done some very basic research
I take it you don't work in the medical field, that you yourself have no medical training of any kind beyond what any of us lay people do. Is that correct?
She says that my Dad is "googling this stuff for 12 hours a day every
day and is now an expert".
I think that my father may really regard himself as some kind of
expert now and feel comfortable directing her care even though he is
definitely not an expert - he has no medical background and again, I
worry that his evaluation skills may be compromised.
Your story does not give me any reason to believe your father's evaluation skills have been compromised or that he is not taking your mother's condition very seriously. I hope that is helpful. With regards to medical background, according to your story the two of you--you and your father--are equal. If anything, he has the edge over you because he has been studying this so intensely. This man does not want his wife to die.
I hope that gives you some peace of mind. Your father is "all there" and he loves his wife like his own life or better. It's the only reason he spends all his waking hours (that he's not caring for her) studying this, obsessing over it. He respects her wishes but at the same time cannot help but read and reread all he can find.
You ask: What can I do?
I'm sorry, but you will have to somehow find the strength to accept the inevitable. Being so far away must eat at your insides. I'm in Canada, too, and I know we have some good counselling services for people struggling with issues like this. It is normal to feel the feelings you are feeling. It is also decent to seek out help at a time like this.
You mentioned Macmillan Cancer Support. I looked them up and you're right; they don't direct anyone's care. They support cancer patients and their families financially and emotionally. It would be inappropriate for them to direct a person's care; the care should be left to the doctor of each patient and if a patient has chosen not to accept treatment, in consultation with their doctor, then the doctor has to respect that decision. Those are the laws and ethics of medical practise as I understand them. Based on your story, I feel confident that your mother has been in deep and serious consultation with her various specialist doctors. I also am of the impression that your father was right there at her side holding her hand, absorbing each word, fearing for himself if he respected her wishes.
What you and your brothers can do is likewise respect her wishes. She has made it clear that she wishes to rest and let nature take its course. Very powerful pain relievers are an option to make her reasonably comfortable so long as she lives. These will most likely be applied as needed. Your father needs the emotional support of his sons at this time. So does your mother.