UPDATE************ Well I have a working solution, although not ideal.
Using the Genesis sandbox child theme which has a mobile nav button built-in, I was able to set that to use the primary nav menu, so that takes care of minimised desktops.
I then added the responsive menu plugin which allowed me to choose my custom mobile menu for the source. Then I hid the plugin for desktop use, and hid the Genesis menu button for mobiles.
Will leave it a few days and then choose who gets the 50 points - thanks to all for your contributions...
(QUESTION RE-PHRASED) Trying to build a mobile version of my site.
2 themes, 1 for desktop and another just for mobile visitors (mobile theme selected automatically for mobile visitors with "any mobile theme plugin").
I have created a custom menu for each theme in wp admin / menus - desktop menu and mobile menu.
With the desktop theme activated I select the desktop menu for the primary navigation. With the mobile theme activated I set the primary navigation to mobile menu.
The problem is that I have to have the desktop theme active for normal operation. Mobile visitors do see the alternative mobile theme, but the navigation always follows whatever the desktop primary navigation is set to.
How can I stop this happening and force the mobile theme to always/only use the mobile navigation?