Conflicting wedding dates?

My fiance and I have decided to have our wedding on June 9th of next year. We have not openly publicized this date yet, but good friends of mine know. Another friend of mine just got engaged and is apparently thinking of June 9th as her wedding date as well. This was brought up in a conversation that I wasn't at, but I guess one of my friends who knew of my date told her, and she is refusing to change her date to accommodate me. We are not really good friends, but we're in the same sorority and she is my little sister, so I am hurt that she doesn't value coming to my wedding and me her's. This also presents the problem that the guests we both invite will have to choose between our two weddings. Anyone have any suggestions on how I can deal with this?