You were starting on the right track but you had several bits of WordPress hookage you still needed to add. An approach I like to use is to encapsulate a call to get_calendar() in a class so we can use the low-level \'query\' hook but only use for it for the one call.

So I wrote up an example which you can drop into your theme\'s functions.php file (or in a .php file for a plugin you might be writing) using a class I named YourSite_Category_Calendar(), and here is how you\'d call it in place of your call to get_calendar():

$cc = new YourSite_Category_Calendar(\'your-category\');
echo $cc->get_calendar();

And here\'s the code for the class:

<?php 

class YourSite_CategoryCalendar {
  var $category;
  var $initial;
  var $echo;
  static function on_load() {
    add_shortcode(\'category-calendar\',array(__CLASS__,\'shortcode\'));
    add_action(\'init\',array(__CLASS__,\'init\'));
    global $wp_rewrite;
    $wp_rewrite->add_rule(\'^events/([0-9]{4})/([0-9]{1,2})/([0-9]{1,2})/([^/]+)/?$\',
      \'index.php?post_type=event&year=$matches[1]&monthnum=$matches[2]&day=$matches[3]&category_name=$matches[4]\',
      \'top\');
    $wp_rewrite->flush_rules(false);  // Remove this after you\'ve got it working
  }
  static function shortcode($attributes) {
    $attributes = wp_parse_args($attributes,array(
      \'category\' => false,
    ));
    $cc = new YourSite_CategoryCalendar($attributes[\'category\']);
    echo $cc->get_calendar();
  }
  static function init() {
    register_post_type(\'event\',array(
      \'hierarchical\'    => true,
      \'label\'          => \'Events\',
      \'public\'          => true,
      \'show_ui\'         => true,
      \'query_var\'       => \'event\',
      \'rewrite\'         => array(\'slug\' => \'events\'),
      \'supports\'        => array(\'title\',\'editor\',\'custom-fields\'),
      \'taxonomies\'      => array(\'category\'),
    ));
  }
  function __construct($category,$initial=true,$echo=true) {
    $this->category = $category;
    $this->initial = $initial;
    $this->echo = $echo;
  }
  function get_calendar() {
    add_filter(\'query\',array(&$this,\'query\'));
    ob_start();
    get_calendar($this->category,$this->initial,$this->echo);
    $calendar = ob_get_clean();
    remove_filter(\'query\',array(&$this,\'query\'));
    list($header,$body) = explode(\'<tbody>\',$calendar);
    $find = \'#(href="http://[^/]+)(/[0-9]{4}/[0-9]{1,2}/[0-9]{1,2}/)#\';
    $replace = \'$1/events$2\'.$this->category.\'/"\';
    $body = preg_replace($find,$replace,$body);
    return "{$header}<tbody>{$body}";
  }
  function query($query) {
    if ($this->category) {
      global $wpdb;
      $find = "FROM {$wpdb->posts}\\\\s+WHERE";
      $add =<<<SQL
INNER JOIN {$wpdb->term_relationships} calendar_term_relationship ON calendar_term_relationship.object_id={$wpdb->posts}.ID
INNER JOIN {$wpdb->term_taxonomy} calendar_term_taxonomy ON calendar_term_taxonomy.term_taxonomy_id=calendar_term_relationship.term_taxonomy_id
INNER JOIN {$wpdb->terms} calendar_term ON calendar_term.term_id=calendar_term_taxonomy.term_id
WHERE calendar_term_taxonomy.taxonomy=\'category\' AND calendar_term.slug=\'%s\' AND
SQL;
      $replace = "FROM {$wpdb->posts} {$add} ";
      $query = preg_replace("#{$find}#Us",$replace,$query);
      $query = preg_replace("#post_type\\s*=\\s*\'post\'#","post_type=\'event\'",$query);
      $query = $wpdb->prepare($query,$this->category);
    }
    return $query;
  }
}
YourSite_CategoryCalendar::on_load();

UPDATE

Based on the comments I\'ve added the URLs rewriting needed as well as a shortcode you\'d call like this:

[category-calendar category="party"]