Really sorry here as i haven’t used any plugin for that yet. I think it doesn’t exists as a complete solution.
But definitely there are plugins that can create sidebar which you can place in your mobile theme (May be you need to place code in your mobile theme’s file).
I actually avoid using sidebar in mobile theme. If i need to, i register siderbar myself keeping some codes in functions.php of theme folder. (You can google register_sidebar + wordpress for some reference). And later you can call that in your mobile theme.