If you're planning this trip like 6 months to a year ahead of time, the plane ticket example is outrageous. For insurance, a reasonable cost is the value of the insured trip multiplied by the chances of the covered event. You can see how cancel for any reason trip insurance would not be very cheap.
I was looking at
travel insurance here and their coverage does include a health emergency of a non-traveling family member that requires you to come home. Allianz travel insurance explains that they cover many (but not all) family members, and used the example that health emergencies of Aunts and Uncles is a covered event, but not cousins. Have you found the particular family relationship is not covered most places?
Another insurer provided this list they consider family:
Insured’s, Traveling Companion’s or Spouse’s:
child;
parent;
sibling;
grandparent, great-grandparent or grandchild or great-grandchild;
son-in-law or daughter-in-law;
brother-in-law or sister-in-law;
parent-in-law;
step-parent, step-child or step-sibling;
aunt or uncle;
niece or nephew;
legal guardian;
foster child or legal ward;
step-grandparent or step-grandchild;
step-aunt or step-uncle.
A way to get around the limits on family would be to invite someone else along. If your Beloved Relative has one of the above relationships to your Travel Companion, you would both be covered for the trip expenses if the Beloved Relative passed or had an extended hospital stay.