How do I add different URL to the HOME link in the breadcrumb for the authenticated user
You could use the theme_breadcrumb hook and change the link for the home breadcrumb by checking the role of the currently logged in user.

I've put some sample code in below, but I am assuming that your breadcrumbs array will always have the 'Home' breadcrumb as the first element.

This code should go in template.php

function yourtheme_breadcrumb($variables) {
  global $user;
  $breadcrumb = $variables['breadcrumb'];

  if (!empty($breadcrumb)) {  

    // Check if the user has the right role.
    if(in_array('your_role', $user-&gt;roles)) {
      $breadcrumb[0] = l('Home', 'path-to-role-homepage');
    } 

    $output = '&lt;h2 class="element-invisible"&gt;' . t('You are here') . '&lt;/h2&gt;';
    $output .= '&lt;div class="breadcrumb"&gt;' . implode(' » ', $breadcrumb) .'&lt;/div&gt;';
    return $output;
  }
}


Hope that helps out.