If I understand your question...CURL
It sounds like you are looking for CURL, Client URL Library Functions.
http://www.php.net/manual/en/ref.curl.php
I have used this to POST to a script on a different server.
I didn't need the result from the POST, but it looks like in your case, you would also need ob_get_contents spoken of at
http://www.php.net/manual/en/function.curl-exec.php in the comments "$retrievedhtml = ob_get_contents();"
If you only need results from the GET method, then use:
$lines = file ('http://www.example.com/get_method?stuff=whatever&otherstuff=blahblah');
I assume you understand the difference between POST and GET methods.
It could get tricky if you have to set and retrieve cookies and intermediary scripts are involved at the remote site. But I would not be quick to say that your task is imposssible.