Change Register/Lost Password “action links” URLs,

I have set up a huge a network multisite for my client which receives 1000's of new users per month and is already 5 clone network sites deep and counting It has a static Home page with the Theme-my-login plugin running on a customised Divi child theme.

On the customised login page there is the login itself which works fine, and below that two "action links" for "Register" and "Lost Password". I have two external custom pages to link to for both links.

So I edit the child theme's functions.php file which already has a few working filters in it handling external authentication, video (popcorn.js), dynamic copyright and hiding the Wordpress Logo from the Admin Bar.

I wanted to change the default Register/Lost Password "action links" to different URLs, change their link titles and Modify the Error pages so that the "Lost Password?" Link would lead to the same URL as the Lost Password "action link".

Below is the Functions.php file before above required changes:

<?php

/*
PHP script content in functions.php of Child Theme in Wordpress Network 
Multisite.

Functions to add new externally authenticated users as wordpress users 
at subscriber level via email field using HTTP POST. 

Usernames expected in the format: user@DOMAIN.com or user@role.DOMAIN.com 
(also all variations of .com.au, .co.nz, etc.) 

New Wordpress Network MultiSite Subfolders are assigned to their own groups of users. 

On login their WordPress profile is automatically created in the MultiSite 
Subfolder for that user; based on the DOMAIN portion of username/email.
Accordingly, Wordpress Network Subfolder names match the DOMAIN exactly. 

eg: "http://wpsite.com/DOMAIN/Home" is the landing page for the user: 
    "user@DOMAIN.com" or "user@DOMAIN.com.au" and so on.

The Logic flow is below annotated and step by step along with the script:

1.Do the external check: The external login must be successful and the return 
  value must be validated with a "200" response from the external auth' server. 

If response is anything else give an error.

2.Do another check to see if they exist in the WP DB, if not; create them
  first (EVERY user in WordPress has a unique ID, so using this ID to identify a user in this script.) 

If the ID is found, our user is automatically logged in 
and lands on their home page.

If the user does NOT exist, the user should be created automatically on the
relevant subfolder site (see notes ablove)
*/

// PHP code starts here:

// The two lines of filters below are executed just before the invocation of the 
// WordPress authentication process.
add_filter( 'authenticate', 'external_auth', 10, 3 );
add_filter( 'login_redirect', 'ds_login_redirect', 10, 3 );

function external_auth( $user, $username, $password ){

    // Make sure a username and password are present for us to work with
    if($username == '' || $password == '') return;    

    // Try to log into the external service or database with username and password
    $args = array(
        'method' => 'POST',
        'timeout' => 45,
        'redirection' => 5,
        'httpversion' => '1.0',
        'blocking' => true,
        'headers' => array(),
        'body' => array( 'username' => $username, 'password' => $password ),
        'cookies' => array()
        );

    $ext_auth = wp_remote_post("http://IP.OF.EXTERNAL.AUTH:SERVER/api-token-auth/",$args);

    // If external authentication was successful
    if($ext_auth['response']['code'] == 200) {

        $userobj = new WP_User();
        $user = $userobj->get_data_by( 'login', $username ); 
        // Does not return a WP_User object :(
        $user = new WP_User($user->ID); 
        // Attempt to load up the user with that ID

        if( $user->ID == 0 ) {
                // The user does not currently exist in the WordPress user table.

                // If you don't want to add new users to WordPress when they don't already 
                // exist; uncomment the following line and remove the create WP user code
                //$user = new WP_Error( 'denied', __("ERROR: Not a valid user for this system") );

                // Setup minimum required user information and create WP user
                $new_user_id =  wpmu_create_user($username, $password, $username); 
                                // A new user has been created

                                // Match DOMAIN in username/email to WordPress Subfolder and add permission to relevent blog 
                $domain_end = explode('@', $username);
                //var_dump($domain_end);
                $match = explode('.', $domain_end[1]);
                //var_dump($match);


                $domain = 'YOUR_DOMAIN.com';
                foreach ($match as $blog_key){
                    $path = '/'.$blog_key.'/';
                    $blog_id = get_blog_id_from_url ( $domain, $path );
                    if ($blog_id != 0) break;
                }       

                //Specify their role 
                $role = 'subscriber';

                // Give the user access to their blog.
                add_user_to_blog($blog_id, $new_user_id, $role);

                // Load the new user info
                $user = new WP_User ($new_user_id);
        } 

    }else if($ext_auth['response']['code'] == 400){
        $user = new WP_Error( 'denied', __("ERROR: User/pass bad") );
    }

    // Comment below line to fall back to WordPress authentication
    // (in case external service offline for maintenance)
    remove_action('authenticate', 'wp_authenticate_username_password', 20);

    return $user;   
}

function ds_login_redirect( $redirect_to, $request_redirect_to, $user )
{
    if ($user->ID != 0) {
        $user_info = get_userdata($user->ID);
        if ($user_info->primary_blog) {
            $primary_url = get_blogaddress_by_id($user_info->primary_blog) . 'index/';
            if ($primary_url) {
                //echo $primary_url; die();
                wp_redirect($primary_url);
                die();
            }
        }
    }

    return $redirect_to;
}

/* Include popcorn.js --------------------- */

function theme_name_scripts() {
    wp_enqueue_script( 'popcorn', get_template_directory_uri() . '/js/popcorn.js', array(), '1.0.0', true );
}

add_action( 'wp_enqueue_scripts', 'theme_name_scripts' );

/* Dynamic Copyright---------------------WPN-10-03-2016--*/

function dynamic_copyright() {
global $wpdb;
$copyright_dates = $wpdb->get_results("
SELECT
YEAR(min(post_date_gmt)) AS firstdate,
YEAR(max(post_date_gmt)) AS lastdate
FROM
$wpdb->posts
WHERE
post_status = 'publish'
");
$output = '';
if($copyright_dates) {
$copyright = $copyright_dates[0]->firstdate;
if($copyright_dates[0]->firstdate != $copyright_dates[0]->lastdate) {
$copyright .= '-' . $copyright_dates[0]->lastdate;
}
$output = $copyright;
}
return $output;
}

/* Remove WP Logo -------------------------- */


function annointed_admin_bar_remove() {
        global $wp_admin_bar;

        /* Remove their stuff */
        $wp_admin_bar->remove_menu('wp-logo');
}

add_action('wp_before_admin_bar_render', 'annointed_admin_bar_remove', 0);

if ( ! function_exists( 'get_custom_header' ) ) {
    // compatibility with versions of WordPress prior to 3.4.
    add_custom_background();
} else {
    add_theme_support( 'custom-background', apply_filters( 'et_custom_background_args', array() ) );
}

?>

Here is the final working code I added just above /* Include popcorn.js --------------------- */ of functions.php after much testing and changing:

/* Filter to redirect register and lost password pages-------------WPN-09-03-2016--*/

function tml_action_url( $url, $action, $instance ) {
    if ( 'register' == $action )
        $url = 'https://EXTERNAL-REGISTRATION-PAGE/';
    elseif ( 'lostpassword' == $action )
        $url = 'https://EXTERNAL-PASSWORD-RESET-PAGE';
    return $url;
}
add_filter( 'tml_action_url', 'tml_action_url', 10, 3 );

/* Filter to change titles of links to above--------------------WPN-09-03-2016--*/

function tml_title( $title, $action ) {
    if ( is_user_logged_in() ) {
        $user = wp_get_current_user;
        if ( 'profile' == $action )
            $title = 'Your Profile';
        else
            $title = sprintf( 'Welcome, %s', $user->display_name );
    } else {
        switch ( $action ) {
            case 'register' :
                $title = 'Not a member? Register';
                break;
            case 'lostpassword':
                $title = 'Forgot your password? Reset it';
                break;
            case 'retrievepassword':
            case 'resetpass':
            case 'rp':
            case 'login':
            default:
                $title = 'Sign In';
        }
    }
    return $title;
}
add_filter( 'tml_title', 'tml_title', 11, 2 );

/* Filter to change link in user error message------------------WPN-10-03-2016--*/

function login_error_message($error){
    //check if that's the error you are looking for
    $pos = strpos($error, 'incorrect');
    if (is_int($pos)) {
        //its the right error so you can overwrite it
        $error = "<strong>ERROR</strong>: Invalid username/password. <a href= https://EXTERNAL-PASSWORD-RESET-PAGE/>Lost Password?</a>";
    }
    else $error = "<strong>ERROR</strong>: Invalid username/password. <a href= https://EXTERNAL-PASSWORD-RESET-PAGE/>Lost Password?</a>";
    return $error;
}
add_filter('login_errors','login_error_message');

Kudos to Igor Yavych who bailed me out while I was making a rookie mistake very early hours of the morning after no sleep last night while experimenting with code to finally get the working result! ( See here: Wordpress PHP issue in functions.php regarding if and else if statement )