External system integration with wordpress

Take a look at what wp_parse_auth_cookie() does. You can easily duplicate that given the fact that you have all the Cookie constants available.

Still, I’d highly advise against that. In your case, I’d try to integrate as far with WordPress as I can to avoid duplicating an authentication mechanism. You can always use any custom code (and connect to external Databases) by using plugins. Simply add the plugin header comment to the bootstrap process of your custom application and you are ready to run. You can also easily display data on custom admin pages or add page templates to the public facing site to handle data entries from there. Then restrict access to the application using is_user_logged_in() or exit( wp_redirect( home_url() ) ); in every other case.

Another option would be to build a custom application and integrate with WordPress via the REST API (available routes + addt. docs). Using WP as simply data provider backend then isn’t that hard.