This really isn't an XPages question. Its more of a server question. What you want to set up is single sign on for multiple servers. Once you authenticate against server #1 you will receive a token / cookie that will allow you to be authenticated against server #2 as well.
Now, granted, you actually can send credentials to the server to authenticate the user fro them, but it is bad design, as you would have to get / store the password (even if you are just storing in ram) which is insecure.
Use the pre-defined methods given to you by domino to accomplish (multiple server SSO).