How do I manage a full desktop version of my website as well as a mobile version?
When you have a full Desktop version as well as a mobile version of the same website, you need to configure your website at the server level so it automatically redirects users using mobile devices.

To redirect mobile users to the mobile site, you need to add a redirection on the website server (usually through a .htaccess file). This redirection serves two purposes:
1. Identifies if the client is on a mobile device
2. If yes, redirect, if not, send to full Desktop page

Unless you are very familiar with .htaccess file set ups, this step is always best handled with the help of your web host provider. As there are sometimes web server specific changes they need to make.

The following link will help provide you with some high level background info on how this set up should work:

http://webdesignandsuch.com/redirect-to-a-mobile-site-with-htaccess-and-set-a-cookie-to-break-redirect/