Emirates make a mistake now we have to suffer

My sister was supposed to come and visit me on Sunday 1 November 2015. Due to a glitch in the Emirates Booking system she was only able to come on Monday the 2nd of November 2015. However, she only has a 96 hour tourist visa. Since the visa was issued for the 1st of November she can now only stay until Thursday the 5th of November. I called Emirates and they referred me to the UAE Emirates service. However, the Emirates service said that my sister would have to pay a 300 AED fine on the airport and wouldn't be able to exit the country if Emirates make a case against her. It would be great if she could stay for one more day. We are receiving no support from the Airline and no one can help us. Highly disappointed.