Ya. It is quite difficult to keep the 2 different menus in different themes. WordPress always keeps active menu in your themes.
So what you can do is,
You can assign your primary menu in your base/desktop theme. And create a new menu like mobile_menu. And keep that menu in your mobile theme using the wp_nav_menu function in your header.php of mobile theme manually.
‘mobile_menu’,’menu_class’=>’your_class’)); ?>
If you still have problem or unable to do so. Do let me know.