Hi Paul,
you need to manage the modules for both menus as a separate instance for mobile, independent from the desktop one of course.
This can be done quickly using the 'Modules manager' you can click to 'exclude from mobile' the current desktop module then click on the 'make mobile' button to assign a new instance to the mobile template. Ensure that menus are instances of the default Joomla menu module 'mod_menu' so that Responsivizer will be able to render as mobile automatically.
If you need help on site to configure it and understand how it works contact me at
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providing an admin account.
John
