Export pages by parent page ID

export.php

/* get the post ID -- you will edit the code below on line 14 ($new_pages[] = {your post id};)
 * open up the live site, edit the file:
 * wp-admin/includes/export.php
 * search for "grab a snapshot"
 * comment out the next line
 * $post_ids = $wpdb->get_col( "SELECT ID FROM {$wpdb->posts} $join WHERE $where" );
 * add the following code right below it.  Save file, run export, then un-comment
 * the original code and delete your inserted code
 */ 

# Export only a particular page and all its children
$post_ids = array();
$new_pages = array();
$new_pages[] = 2; # Parent page ID, which we will export, along with all its children
while (count($new_pages)) {
  $where = "WHERE post_parent IN (".join(',', $new_pages).")";
  foreach ($new_pages as $np) {
    $post_ids[] = $np;
  }
  $new_pages = array();
  $new_pages = $wpdb->get_col("SELECT ID FROM $wpdb->posts $where ORDER BY post_date_gmt ASC");
}
# $post_ids array now contains the pages we wish to export