You can add the following to your functions.php
to achieve what you are after. The action init
doesn’t seem to fire in time for what you are looking for.
if($_GET['action']==='rp' && strpos($_SERVER['REQUEST_URI'],'wp-login.php')) {
$key = isset( $_GET['key'] ) ? $_GET['key'] : '';
$login = isset( $_GET['login'] ) ? $_GET['login'] : '';
wp_redirect( site_url( '/reset-password/' ) . '?key=' . $key . '&login=' . $login );
exit;
}