Random posts that always include a particular post?

Try this code::

post__in (array) – use post ids. Specify posts to retrieve. ATTENTION If you use sticky posts, they will be included (prepended!) in the posts you retrieve whether you want it or not.

<?php
    $parent = $post->ID;
    $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
    $query_args = array(
      'post_type' => 'page',
      'post_in' => array('post_id_to_include'),
      'posts_per_page' => 3,
      'orderby'   => 'rand',
      'post_parent' => $parent,
      'paged' => $paged
    );

   // create a new instance of WP_Query
   $wp_query = new WP_Query($query_args);
?>