What is it about your position that is better suited to tell her her calling and the facts of the situation than her and her mother?
Honestly, if you were my “friend” and you decided to lecture me about my personal situation and what you thought I should be doing with my mother, I would probably tell you to mind your own business.
Spiritual work of mercy: to admonish the sinner
Although on the one hand you two might have a point if the 89-year-old mother is sprightly and totally able to take care of herself, getting groceries and cooking, if in fact the mother, at 89, is in need of help, there seems only to be a daughter-in-law (where is the son?) who is currently already caring for her own mother.
If the son, who would be the daughter’s brother, is in the picture, then he should definitely be brought into the conversation. OTOH, he may be dead or otherwise unable to help in the care of elderly parents.
If the mother does need help, and the missionary daughter is the only one available, I think that pointing out the downsides of not caring for her mother would be the right thing to do, even on the part of a friend.
Additionally, ArcadiAnna may have some insight into her friend’s state of mind.
Maybe the friend is very focused on the missionary work because she believes that God does call on us to completely abandon our families without making proper arrangements for them but is conflicted.
Maybe ArcadiAnna knows the friend well enough to know that her friend will regret not doing this.
So I don’t think we should just assume there is something wrong with what is happening here.