I would think the airlines would provide a companion fare, even for a recreational visit, especially if you do a turaround and your sister's doctor provides some kind of confirmation that it's medically necessary that she be accompanied. Our local disabled van service doesn't charge the $3 fare for the companion.
Not sure this is relevant, but my cousin is on Social Security because she is technically disabled due to metastasized cancer.
Social Security pays for her and her companion's transportation to medical treatments, hotel rooms, and meals. In her case she flies from Southeast Alaska to Seattle for treatment as there are no oncologists in SE Alaska, not even in the state capital, Juneau.
But I also remember someone who flew RT New York to Sydney to accompany children for visits with the other parent. (There are, or were at the time, no unaccompanied minors on international flights.) Other parent flies RT Sydney to New York to return the kiddies. No discounts, just a lot of inconvenience, and many, many ff miles.
Your parents were very wise to create the trust, and you are doing a remarkable job as caregiver. It would be nice if your other sister could be the companion on the return flight, but sometimes that isn't practicle. I'm glad you enjoy flying!