You can share user tables between different WordPress installations by installing the second site ("Site B") to use the original site's ("Site A") database, then choosing to use an alternate table prefix during installation so as to keep the rest of the data separate.
The second part of the problem is sharing login cookies between the two installations (what WordPress uses to keep track of login/"session" data). In order to do this, you must use the same cookie-path for both sites.
After installation, open the
wp-config.php file in Site B's installation root, and add (or replace) the following lines shortly after the database configuration, modifying them as needed to fit your configuration:
$cookiehash = md5("http://www.bradleycountypulse.com/"); // Use Site A's URL
define(CUSTOM_USER_TABLE,'wp_users'); //Change 'wp' to match the prefix set during
define(CUSTOM_USER_META_TABLE,'wp_usermeta'); // Site A's installation
define('COOKIEPATH', '/'); //This path should reference Site A's root
define('SITECOOKIEPATH', '/'); //Should match 'COOKIEPATH'
define('COOKIEHASH', $cookiehash );
Note that this will only work if the two installations reside on the same domain (which yours do!).
An alternate solution would be to setup the entire system as a single multisite installation.
Still another solution (albeit one that requires more legwork) would be to employ custom page templates on a single installation.