Hi, Anon. I am sorry to hear about your mother's illness. I am sure it is stressful for everyone, including you.
I faced a similar dilemma with my wife's parents. Both were in their 90s, and pretty frail, and we thought we should avoid causing them stress by coming out to them. I was full-time, but I didn't go with my wife when she went to visit, so it wasn't an issue.
But, as their health continued to decline, we realized that, sooner or later, there would be a funeral. I felt that it would be wrong not to attend, but I just couldn't bring myself to revert to male mode for the occasion. And it would have been very wrong to come out at the funeral. So we decided to tell them.
It couldn't have gone better. My wife told them, and some time later, I went with her for a visit. They were both amazingly accepting. They got my name right every time. There were a couple of pronoun slip-ups, but they corrected themselves. My MIL even gave me a beautiful gold necklace.
After my MIL eventually passed on, my FIL would phone to talk to my wife. If I answered the phone, he made a point of addressing me by my name every time. It was a beautiful display of support by a real gentleman. He has since passed on, too. But they both got to meet the real me.
I tell you my story to show that, although it is easy to fear the worst, the reality may be much better, even with elderly parents.