As someone who is a part of the "modern medical establishment", I've followed this thread with interest. I feel for you about your mother's progress -- happy that she has lived longer than projected, sad that her condition has progressed worse.
Addressing a couple things that have baffled your doctors:
"How long do they have to live?" is a common question in the medical field, and for a lot of us it's one we dread. It's a question that often requires something that most physicians don't have. A crystal ball. Physicians that I have worked with often precede their discussions that they honestly cannot predict how long a family member will live, and that they can give an educated guess but by no means should it be considered a deadline. 3-5 years is, by the book, the median length of time between diagnosis and death. Many fall within that range, and many do not. Lou Gehrig himself lived for 2 years after being diagnosed. One of the premier pathology lecturers for the USMLE (the board exam that all physicians must take) claims to have been diagnosed with Lou Gehrig's Disease, only for the disease to regress. While rare, it's not unheard of. If your physicians are indeed baffled that your mother has lived longer than the textbook's stated median, they need not be.
Regarding whether your physicians know that your mother is suffering from ALS or not, I cannot pretend to know the situation but I can venture some guesses from my own experiences. As you have mentioned, autopsy is the only definitive way to diagnose that a person is suffering from ALS, lest a patient undergoes a nerve biopsy while still alive. So it becomes largely a clinical diagnosis. With a disease like ALS, it's sometimes hard to appreciate that the differential diagnosis is quite large. Certain diseases that mimic ALS are reversible, and are emphasized throughout this thread by people who believe from experience that the cure is a Tetracycline (more likely the patient had Lyme Disease) or Vitamin B12 (more likely the patient had Vitamin B12 deficiency). It's no intended disrespect to you, but I just have to question whether your physicians are "baffled" in their diagnosis, or whether they are just trying to double-check/triple-check/quadruple-check that they aren't missing a treatable diagnosis.
But on the subject of one of the more popular replies in the thread, if I tell a patient that they have an untreatable disease and they respond with "F you, I'll find my own treatment", I (and I would hope that most doctors) would be supportive and try to assist in that search. Truth is that allopathic medicine doesn't catch it all, and you never really know what might work. Some of the methods described in this thread did seem to provide temporary relief, and that's pretty important to not miss. With a disease deemed "currently untreatable" like ALS, no one should hold their patients back from trying anything.
I wish you and your mother the best, and I hope that she does get to see you at your graduation.