Did you read my post about using extra menu short codes inside a [show_if device='xxx'] shortcode.
You can use the primary (or secondary) menu for desktop by hiding it on mobile with the Hide Area > Hide: desktop option, then insert the mobile menu in an insertion area inside a [show_if device='mobile'] shortcode.
If you need help with the details, give us a link to a page explaining in detail which menu needs to change on mobile and how