problem with Cookies and domain redirects

[Bridget_Almas]

I'm using the LWP modules in order to redirect users to a new url while
hiding the parameters from their original form submission, and am having
trouble getting the cookies set by the response to be set in the proper
domain.

   So, for example, the user submits a form, which posts to

   http://domain1.com/mycgi.cgi

   I take that, read in the input parameters, and transform it to a new url
   (at a new domain):

   my $newUrl=http://domain2.com/mycgi.cgi?param1=x&param2y
   my $ua = LWP::UserAgent->new;
   my $cookie_jar = new HTTP::Cookies;
   $ua->cookie_jar($cookie_jar);
   my $request = HTTP::Request->new('GET' => $newURL);
   my $response = &request($ua, $request);
   my $html = $response->content;
   print $response->headers_as_string;
   print "Content-type: text/html\n\n";
   print $html;

The response includes several Set-Cookie headers, which are being accepted
by the browser, but they're being set in the domain of the original url
(i.e. domain1.com) instead of the newUrl (i.e. domain2.com), and thus are
ignored by subsequent posts to the cgi running at domain2.com.

Does anyone know of a way to get the cookies set in the domain of the 2nd
url?

Thanks.
Bridget Almas