Although it would be useful to determine why the extra notifications are sent (forwarding settings?), there is a way to adjust who gets notification emails when a comment is posted (which is what you asked, not how to fix the problem):
// adds emails to the 'notify admins on comment submit'
// from http://www.sourcexpress.com/customize-wordpress-comment-notification-emails/
// must be enabled via Settings, Discussion, "Email me whenever Anyone posts a comment"
function ss_comment_moderation_recipients( $emails, $comment_id ) {
// Email notification only to the admin
$emails = array( get_option( 'admin_email' ) );
$emails[] = "[email protected]";
$emails[] = "[email protected]";
return $emails;
}
add_filter( 'comment_moderation_recipients', 'ss_comment_moderation_recipients', 11, 2 );
add_filter( 'comment_notification_recipients', 'ss_comment_moderation_recipients', 11, 2 );
The $emails array is an array of emails to send to. The code above gets the admin_email email address, then adds two emails to it. The two add_filters are needed to ensure it works.
Based on the answer here: http://www.sourcexpress.com/customize-wordpress-comment-notification-emails/