Yup, this is a good one. The bane of my existence. ;)one of my top 3 triggers that sends me into total psychological overload is being unable to meet other people's competing needs.
I try to assign priorities. With regard to family, this would be my kids, then my elders; but if someone is ill, then that person might become a priority -- no matter what else was planned. If your mother can't understand this, or won't, it's not worth trying convince her. It's common sense to support those who are sick, first and foremost; plays and most other activities are a much lower priority.
If you have multiple illnesses to deal with, one possibility is divide and conquer; but it largely depends upon the nature and severity of the illnesses as well. If UB is that ill, then I would say that he is the priority. Your mother may need some medical attention, but it can wait -- regardless of how she feels about it.
Since you and your husband are the ones responsible for taking care of everyone, y'all get to make the decisions, and if others don't like it, it is their problem. This is not being selfish; this is being practical, trying to do the absolute best you can with difficult and complex circumstances, and completely impossible expectations from others.
I finally learned, with regard to my mother, that I'll never be able to make her happy, no matter what I do, what decisions I make. It will always be hit or miss with her, depending upon how it strikes her expectations. More importantly, I'm not responsible for making her or anyone else happy, just as no one is responsible for doing that for us (would that this were possible ;) ).
If you crash and burn, who will take care of UB or your mother then? Your kids? Therefore, by logic, you must be allowed to manage your "ship", damn other people's feelings and expectations when overwhelmed. Because, obviously, no one is caring much about your feelings and needs by making demands that you can't meet.
I know all of this is easier said than done, but it is possible. I will likely long have the underlying feeling that I'm a jerk because I think in this way, now, but at least I'll be a jerk with my sanity. ;)