Display child pages full template including the content

I would try setting up post data in the loop and then calling a page template using get_template_part function. Note: depending on theme it may produce some unexpected results, as page template sometimes also includes site header and footer. But it’s something to get you started.

$getchilds = array(
    'parent'        => $post->ID,
    'child_of'      => $post->ID,
    'sort_column'   => 'menu_order',
    'sort_order'    => 'ASC'
);

$postlist = get_pages($getchilds);

foreach ($postlist as $post) {

    // setup post data, so page template will use it as a "master" post
    setup_postdata($post); 

    // we get page template name for the post and remove ".php" at the end to make it work
    $template = preg_replace("/\.php$/", "", get_page_template_slug($post) ); 

    // now let WordPress fetch that page for you
    echo get_template_part($template);        
}