How pull in other pages’ templates and content and output those on a “combining” page?

Imagine I have the following setup:

* Combining Page (Template: Combine Template)
    * Sub Page 1 (Template: Basic Template)
    * Sub Page 2 (Template: Other Template)
    * Sub Page 3 (Template: Basic Template)

So I have three sub pages, two of which have the same template (which uses custom fields as well as regular content). I want the parent page’s template to be able to work like this:

PSEUDO-CODE:

//Show the content for this combine page (e.g. a title)
if ( have_posts() ) : while ...this is the main loop...

$wp_query = new WP_Query();
$all_pages = $wp_query->query( array( "post_type" => "page", "posts_per_page" => -1 ) );

//Get child pages
$child_pages = get_page_children( $post->ID, $all_pages );

//Loop through child pages so we can add their HTML (made from applying their content to their templates)
foreach( $child_pages as $child_page )
{
    /** WHAT DO I DO HERE? **/
    //Pseudo code
    $child_page_template = get_page_template( $child_page->page_name );
    $child_output = apply_to( $child_page_template, get_page_content( $child_page->content ) );
}

EDIT
In addition, on the child page, I get a custom field and loop through it:

$values = get_post_custom_values( "mycustomfield" );
foreach ( $values as $value ) echo $value . "<br>";

END EDIT

How would I do this?

Is there anything built in to do this? Or would I need to use output buffers to isolate everything and print each to a buffer from within a function?