How can two browsers connect using the same session ID

[2pac]

I have an application that will spawn multiple clients. All of the
clients need to automatically login into a website and do GETs
The website (not under my control) has a J2EE based application server
and provides a session ID to each client.It does not allow
simulteanous access from two different clients(presumably on different
IPs) with the same session ID
Am wondering how can I write an application that will ensure that each
client can login simulteanously with the same session ID.
one solution is to have a proxy that establishes a connection to the
website.
The clients are hidden behind the proxy and send request to the proxy.
The proxy will then forward connection to the website using one single
session ID
are there any better ideas?
What is the best way to implement this?
Any suggestions appreciated
Thanks