My mom died of cancer in the middle of my third year of post-graduate studies.
I'm female in a (heavily at the time) male-dominated field, and I did try to put up a strong front for that reason. Even so, I wouldn't have drempt of keeping such important information from my advisor, especially as I had to take lots of unexpected days off intermittently as she was in and out of the ICU (in a country about 11 hours from where I was.)
My best advice is that you do what you won't regret later. I tried to fulfill my obligations to my studies as well as to be there for my mother (who was close to death several times.) My biggest regret is that I waited too long before finally asking to take (and being immediately granted) a leave of absence. My mother died before I even left to go to her.
My deepest sympathy for what you are going through. As someone else said, think about yourself and your mother, and do what's best for the both of you. The rest will fall into place.