Your sister will be angry but I doubt she'll "hate you forever". Have you tried explaining this to the people in charge of both performances? They cannot change the dates, I am sure, but a little advance warning and explanation will go a long way in terms of preventing at least the social suicide aspect of it.
Also - ask your sister (very, very
nicely) if something happens at the band gig, can she tell them that you're otherwise engaged? Someone interested in your band will be interested in hearing you if they are told - there is another way we can sound.
Big, big hint - being discovered is nice. Really, really nice. It is also really, really rare. I get the feeling that the school thing will not be repeated, whereas your chance to be in front of some important folk in the music biz just might be, particularly if you are good and you are on good terms with the people who book the venues.
Just a thought.