Add an option for nav menus for new child pages of contained parent pages to be automatically added as sub items under that page in the nav.

. pfxwp_nav_option_auto_add_subpages.php

<?php



//
//  ADD OPTION IN wp-admin/nav-menus.php
//

#\pfxwp\hook::add_filter_after( 'pre_option_nav_menu_options', 'gettext', 'pfxwp_nav_option_auto_add_subpages' );
add_filter( 'pre_option_nav_menu_options', 'pfxwp_nav_option_hook' );
function pfxwp_nav_option_hook( $v ) {
	remove_filter( 'pre_option_nav_menu_options', 'pfxwp_nav_option_hook' );
	add_filter( 'gettext', 'pfxwp_nav_option_auto_add_subpages' );
	return $v;
}

function pfxwp_nav_option_auto_add_subpages( $translations ) {
	if ( 'Automatically add new top-level pages to this menu' === $translations ) {
		remove_filter( 'gettext', 'pfxwp_nav_option_auto_add_subpages' );

		global $nav_menu_selected_id;
		//$nav_menu_selected_id = isset( $_REQUEST['menu'] ) ? (int) $_REQUEST['menu'] : 0;

		$auto_add             = get_option( 'nav_menu_options' );
		if ( ! isset( $auto_add['auto_add_subpages'] ) )
			$auto_add = false; 
		elseif ( false !== array_search( $nav_menu_selected_id, $auto_add['auto_add_subpages'] ) )
			$auto_add = true;
		else
			$auto_add = false;

		$r = '';
		$r .= $translations;
		$r .= '</label></dd>';
		$r .= '<dd class="checkbox-input">
		 <input type="checkbox"' . checked( $auto_add, true, false ) . ' name="auto-add-subpages" id="auto-add-subpages" value="1"> 
		<label for="auto-add-subpages">Automatically add new subpages to this menu</label>
		</dd>';

		return $r;
	}

	return $translations;
}


\pfxwp\hook::add_filter( 'wp_update_nav_menu', function ( $nav_menu_selected_id ) {
	if ( ! $nav_menu_selected_id )
		return;
	$auto_add        = ! empty( $_POST['auto-add-subpages'] );
	$nav_menu_option = (array) get_option( 'nav_menu_options' );
	if ( ! isset( $nav_menu_option['auto_add_subpages'] ) )
		$nav_menu_option['auto_add_subpages'] = array();
	if ( $auto_add ) {
		if ( ! in_array( $nav_menu_selected_id, $nav_menu_option['auto_add_subpages'] ) )
			$nav_menu_option['auto_add_subpages'][] = $nav_menu_selected_id;
	} else {
		if ( false !== ( $key = array_search( $nav_menu_selected_id,
		                                      $nav_menu_option['auto_add_subpages'] ) )
		)
			unset( $nav_menu_option['auto_add_subpages'][ $key ] );
	}
	// Remove nonexistent/deleted menus
	$nav_menu_option['auto_add_subpages'] = array_intersect( $nav_menu_option['auto_add_subpages'],
	                                                         wp_get_nav_menus( array( 'fields' => 'ids' ) ) );

	update_option( 'nav_menu_options', $nav_menu_option );
} );

///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////




/*
Based on Auto Submenu Plugin by Jamo Web Creations
http://jamocreations.com/en/artikelen/auto-submenu
*/
class AutoSubmenu {

	/**
	 * Constructor
	 */
	function __construct() {
		add_action( 'publish_page', array( &$this, 'on_publish_page' ) );
	}

	/**
	 * When publishing a new child page, add it to the appropriate custom menu.
	 */
	function on_publish_page( $post_id ) {

		// Theme supports custom menus?
		if ( ! current_theme_supports( 'menus' ) ) {
			return;
		}

		// Published page has parent?
		$post = get_post( $post_id );
		if ( ! $post->post_parent ) {
			return;
		}

		// Get menus with auto_add enabled
		$auto_add = get_option( 'nav_menu_options' );
		if ( empty( $auto_add ) || ! is_array( $auto_add ) || ! isset( $auto_add['auto_add_subpages'] ) ) {
			return;
		}
		$auto_add = $auto_add['auto_add_subpages'];
		if ( empty( $auto_add ) || ! is_array( $auto_add ) ) {
			return;
		}

		// Loop through the menus to find page parent
		foreach ( $auto_add as $menu_id ) {
			$menu_parent = null;
			$menu_items  = wp_get_nav_menu_items( $menu_id,
			                                      array( 'post_status' => 'publish,draft' ) );
			if ( ! is_array( $menu_items ) ) {
				continue;
			}
			foreach ( $menu_items as $menu_item ) {
				// Item already in menu?
				if ( $menu_item->object_id == $post->ID ) {
					continue 2;
				}
				if ( $menu_item->object_id == $post->post_parent ) {
					$menu_parent = $menu_item;
				}
			}
			// Add new item
			if ( $menu_parent ) {
				wp_update_nav_menu_item( $menu_id, 0, array(
					'menu-item-object-id' => $post->ID,
					'menu-item-object'    => $post->post_type,
					'menu-item-parent-id' => $menu_parent->ID,
					'menu-item-type'      => 'post_type',
					'menu-item-status'    => 'publish'
				) );
			}
		}
	}
}

$auto_submenu = new AutoSubmenu();