Erratic Schedule and Pay Errors

I have two questions. The first pertains to having a set schedule, and the second pertains to correcting wage errors. My mother works in the activities department of a nursing home for little more than minimum wage. Aside from her supervisor, she is the only 40 hour employee. There are two other 32 hour employees.

Questions 1: Each employee is supposed to work every third weekend, receiving the preceding Friday and following Monday off. Holidays are rotated among the three employees as well. The two 32-hour employees frequently request their weekends off, and my mother's schedule is shifted to cover their time. Also, she is frequently scheduled to work their holidays. Her own requests for weekends or holiday time off are denied, as her supervisor tells her she has already granted the other employees' requests (even if my mother asks several weeks in advance). She is able to take her vacation time, but never around the holidays she is supposed to have off. She is increasingly frustrated about covering these other employees' hours as her schedule is constantly changing. Her supervisor frequently tells her that the other employees' need more time off for their families and husbands (even though one employee has college age children). My mother is divorced and my brother and I are out of college. I feel as though she is being targeted because she is single and does not have kids at home, though her supervisor and the facility director are both female as well). Does she have any recourse for dealing with this erratic schedule other than finding another job?

Question 2: When the nursing home is not fully occupied by residents, my mother is required to take unpaid hours off each week (the number of hours depends on the number of empty beds). The facility director verbally stated that employees could use excess sick pay to cover those hours. Over the Thanksgiving pay period my mother had to take 5 hours off, and opted to use sick pay for those 5 hours. This was clearly marked on her schedule. Additionally, she was approved to take the Friday after Thanksgiving off as a vacation day. When she received her pay check she was only paid for 1.5 hours of sick pay and was not paid at all for her vacation day. She received her pay check on Thursday and reported the error on Monday. Her supervisor and the facility director acknowledged the error, but said they could not issue a check for the missing pay: she would have to wait until the next pay period and it would be added to that check. Is that acceptable? The facility director said paying her before that date would cause errors because the end of the year was approaching and extra vacation days would "cash out" then. (The explanation was not clear to me).

Thank you for your time.