How to add extra menu source and access it in a theme
To be able to put it in a theme variable I think you're looking at something like the following.  Please note I haven't tested this, but i should put you in the right direction.

In your template.php or a module:

function MYTHEME_preprocess_page($vars){
  $global_menu = menu_navigation_links('menu-global-menu');
  $vars['global_menu'] = theme('links__menu_global_menu', array('links' =&gt; $global_menu));
}


Then clear your theme registry/caches.