I would have insisted to be flown or hospital transport of some sorts. Seems the OP has put themselves in jeopardy from the get go, seems very irresponsible.
In defense of anyone will an ill family member. Insurance does not cover transportation to health care. Mobile health care transportation companies are cost prohibitive for many and expecting any insurance company to pay for flying them well that's just ludicrous.
I took my friend's wife with advanced stage cancer to Tampa several times in my MH because it was much more comfortable for her to travel in.
THIS is what I would question:
New Mexico to Mayo clinic in Phoenix, AZ 7 hours
New Mexico to Mayo Clinic in Florida 26 hours
Even if one specializes in one particular area, Mayo would not insist you go there because they share all information. So there would be no need to drive that far.
