Mayo does have certain specialties and they do treat rare diseases. There is a thread on Mayo Clinic Connect about why its so hard to get an appointment:
https://connect.mayoclinic.org/discussion/cant-get-an-appointment/?pg=7
Persistence and perhaps some testing to support your appeal may help but there is a long waiting list. This may well be the rare disease above which might help get their attention but your mother needs treatment now. So a double pronged approach to get diagnosis now while trying to get accepted to Mayo may be the way to go. Also if there is another university medical center near you that is worth exploring. Nothing is easy about health care these days. Let us know how things go!