I appealed for skilled care for my father.  Medicre declined skilled nursing rehab after the facility reported  no improvement after 2 weeks.  I completed the appeal form and won on a technicality.  I made my appeal a day before July 4th and the facility had to respond in 24 hours.  Since that included the holiday, the deadline was not met and my dad got another 2 weeks.
Is your mom able to do physical therapy?  If so, that should qualify her for at least a week or two of skilled nursing care.  Other things that would qualify her would be IV therapy or injection, wound care...anything that requires a LVN or RN rather that a general caregiver.  Unfortunately, not being able to go to the restroom or bathe herself doesn't qualify.  I would focus on the physical therapy.  Unfortunately, since my Dad did not progress with physical therapy, he ended up having to go to a nursing home.