Please do not let your family define your responses. Your sister seems to be laying on the FOG fairly thick. And the neighbor is just interfering in something where she is not aware of all that is involved.
I agree FOG... .FOG... .FOG... .
The drama triangle is there too... .Your mom the victim, you the persecutor, friend/sister the rescuer or Your mom the victim, friend/sister persecutor, you the rescuer... .depending on how you look at it.
I also want to say that it is not selfish to take care of yourself, it is self care... .I say this because it's true and sometimes you need to hear it from someone else.

Think about this situation in terms of yourself, not what your sister thinks you should do, or the friend, or society... .what is right for
you.
It sounds like your mom is getting appropriate treatment and the diverticulitis has not developed into anything more serious. What will your being there change?
Panda39