3rd party cookie, in the context of a web page, is where the web page directs the web brows to load content, such as an image, from another web server. Any cookies attached to that included content are considered 3rd party.

What your portal is doing is actually proxying. The browser sees the cookie coming from your portal. Also, it's possible the cookie has encoded the IP address of your portal in it, so the secure website might reject the cookie because the web browser's IP address won't match the IP address encoded in the cookie.

What you need to do is make the web browser always access the secure website through your portal. One way to do this would be to enhance your portal to re-write the URLs in the responses from the secure server so that they refer to the portal. Then the portal needs to forward further requests from the browser to the secure site. There are several http proxy examples on CPAN.

Alternately, your company's IT dept can redirect requests for the secure website to your portal. Of course, your portal will still have to properly forward requests and responses.