This might be a great time to get some dynamic alumni or national reperesentatives involved! Having an older (and hopefully mature) person's input on how to solve the issues can bring a fresh perspective to the group. Who know, but they might have dealt with very similar issues during their undergraduate years!
Also if smaller cliques are really beginning to dominate the chapter organizing activities where members are paired up with sisters they don't know as well (not necessarily placing enemy A with enemy B) might help break down some of the barriers among the group. During a chapter meeting make an effort to recognize members for accomplishments that they have achieved -- let every young woman know that their sisters are proud of them for being invited to join an academic honorary, for scoring the winning basket in a school athletic event, or for organizing an event for Habitat for Humanity.
Discourage the rumor mill. If rumors are circulating that the chapter might lose its charter, have the officers address this at a chapter meeting. Don't partcipate in sister-to-sister gossip about the activities of another member or on the organization's financial programs.