I figured out how to copy over the main menu to "mobile_menu" and assign the modules properly, but there's a problem with the menu item names. For example, the first link is called "News" on the main menu. On the new copy (the mobile menu) it says "News (2)". I tried to change the name to simply "News" as it is on the main site, but I get the error:

Save failed with the following error: Another menu item has the same alias in Root. Root is the top level parent

Which I understand in theory. But what the heck would be the right way to do this? Thanks very much,
Bill

Found a solution. It doesn't matter if there are multiple menu item names in the same root. I found that all I have to do is change the ALIASES to something different.

So, in my main menu the first menu item is "Home" and the alias is "home".
In my mobile menu, the first menu item is also "Home" but I made the alias "home-mobile".
Worked like a charm. Hope this helps anybody else that might have this issue.

Can you post your mobile site? I'd like to see what you'r talking about.