Hi,
I read on another forum post that I could just re-register the custom post type in the functions of the wptouch plugin, but I tried and it still did not work. Could you tell me the exact file location to register the plugin?
Yes, you can try doing that. Though please keep in mind that in WPtouch (free), any changes done to the core files will be overwritten in an event of an update. In WPtouch Pro, since it supports child themes, changes/customizations will be able to survive upgrades.
The location of the functions.php file in WPtouch (free) is /wp-content/wptouch-data/themes/bauhaus/default/functions.php.