This gist contains code-suggestions to allow for a Moodle-theme to detect IFRAMES, and accordingly use a PHP-flag to hide blocks within the theme. Using that PHP-flag, allows you to use the same theme for Moodle-administration (by accessing the Moodle application directly), as well as for wrapping things within Joomla!.
The technique involves setting a cookie from both the Moodle-theme (using JavaScript) as well as the Joomdle component (using PHP). The cookie will then be used within the PHP-code of the Moodle-theme to hide columns - how to do that part depends entirely on the code of your specific Moodle theme. Note that the cookie is initialized on purpose with a lifetime of 0 (browser-session related) and a path of / (assuming both Joomla! as Moodle are installed in the same domain).
Place this PHP-code within the components/com_joomdle/joomdle.php file just after the defined()-check
setcookie('joomdle_iframe', 1, 0, '/');