With the Ethernet shield, the Arduino can be a server that knows how to handle GET requests, or a client that knows how to make GET requests.
With a bit of care, the Arduino can act as both client and server, though it is not easy to cram both roles into the limited memory you have to work with.
Forget the Arduinos for now. Get one PC, running Apache so it can be a server and a web browser so it can be a client, to communicate with another PC running Apache so it can be a server and a web browser so it can be a client.
Once that works, with appropriate scripts on both servers, making the Arduino act as server and client will be trivial.