Caring for an ill family member often requires taking on the role of "decision maker." Sometimes it's multiple mundane decisions (Should you ask your sister to do the shopping? Is this a good day to shower Mom? Now or after lunch?). And sometimes it's several important health decisions, all in a short period of time.
Every decision is brain work
Decision making involves considering options and looking at tradeoffs, and then making a choice. Research has found these are particularly demanding mental tasks. So when you have a lot of decisions to make over the course of a day, your brain gets weary. That is called "decision fatigue."
Decision fatigue affects our behavior
You are unlikely to feel your brain's fatigue; it's not like physical fatigue. But weary brains, like weary bodies, get lazy. In fact, a weary brain resists expending all the energy that is required to make a careful decision.