Hi Katy,
I cannot imagine the emotional distress you must be feeling at this point. My only advice is that you tell your mum that you love her. She knows this, but hearing it always makes a difference. She will understand your situation and knows that if you could stay, you would.
While you cannot be there, phone her in the days she has left, and tell her you love her. Every day - several times a day if you can.
My dad was just as stubborn as your mum sounds, convinced that he would get better, and he put up a good fight! There is no real way you can say goodbye, because that would mean that you have given up hope, even if the inevitable is approaching, I always held out for some miracle.
I am comforted by the fact that I was able to tell my dad every day that I loved him, and knew that he loved me with all his heart, just as dearly. I think that's all a parent needs to know and hear in these very hard and dark days.
Knowing they are loved by their children is all the thanks they need.