Alphabetize all but one category

Add an else to the condition along with adding the excluded category id in the is_category() call. You will also need to include/exclude that particular category depending on the condition that is true:

NOTE: you probably want to avoid using query_posts and use WP_Query() Reference here

 <?php 
    if (is_category(15)) {
        $posts = query_posts($query_string . '&orderby=date&order=asc&cat=15'); 
    }

   else {
     if(is_category()) { 
        $posts = query_posts($query_string . '&orderby=title&order=asc&cat=-15'); 
       } 
   }
 ?>