Adding “redirect” to a button

You will need to use a hook (such as init or admin_init) to detect whether a condition has been met. For instance, the existence of a certain querystring variable (which can be a url encoded url, if you like).

When the condition is met, use wp_safe_redirect() (and optionally exit()) to redirect to the URL you want. You can either hard-code that URL or fetch it from the querystring if your button passed it along as a urlencoded variable.

Hypothetical example (PHP 5.3+ syntax):

add_action('init', function(){
    if ( isset($_REQUEST['redirect_to']) ) {
        wp_safe_redirect($_REQUEST['redirect_to']);
        exit();
    }
});