It’s a difficult situation all round for everyone.
Living with cancer is hard work, and it sounds like your mother is trying to make the best of a bad job.
My mother never owned a washing machine and didn’t think it was necessary to scrub, soak and then place soiled clothing in the washing machine, she didn’t get rinsing plates to put in the dishwasher either, but we all do things differently, as I’m sure when your 19year old daughter will in time, do things differently to you.
Its not easy watching anyone succumb to dreadful life changing conditions, it’s even harder watching someone you love go thru it.
Perhaps get a piece of paper and write the irritating things down, I’m sure if she read them, she would try and change her irritating habits, you may find out that she gets pissed off with a couple of your habits too.
I wish you and all your family the very best of luck and hoping that 2023 is kind to you all.