How to use Drupal to encapsule an external site
If you've, at least, any control on the second web site you can do it with dynamic includes. It works not so bad with the help of an own module.

The idea its to create a module that do a file_get_content() and return it to Drupal that gonna show the content.

But, for it your second web site should have relative paths between his pages, or you will make the change with a regex.

There an example module, no tested.

function mymodule_menu() {
  $items = array();

  $items['inc/%'] = array(
    'title' =&gt; t("Include"),
    'page callback' =&gt; 'mymodule_include',
    'page arguments' =&gt; array(1)
  );

  return $items;
}

function mymodule_include($path) {
  $http = 'http://example.com/';
  // Maybe check if the page is available 
  // better to use drupal_http_request for that
  $content = file_get_contents($http . $path);

  // Perform any change in the content before to
  // send it for render.
  return $content;
}