John, John, John, where do we begin? Is this a live app, or just a proof of concept type scenario.
One thing that makes me a little nervous is asking a user to log in. One of the reasons for using the portal is the ease with which we can delegate the task of user management to the portal. You should use the portal to log the user in, taking advantage of the massive user management facilities provided through the portal. I believe the request object has a method that gives you the name the user used to log in.
Now for the idea of one portlet calling on another portlet. You're thinking in too much of a Struts/JSF/Servlet state of mind. This isn't really how portlets are supposed to work. I mean, you want the portlet the user used to magically disappear (I don't think that's possible), and then have two new portlets just add themselves to the same portal page, and display with information provided from the first portlet. I think you're going to have to redesign the portal to achieve this. It's not supposed to work that way.
I don't mean to be trite, but you really have to change your thinking when you move to the portal.
Here's what I might do, if you are totally committed to not using the portal user management facilities.
Create a portlet that logs the user on. Have three JSP pages: one is the landing page (index.jsp), the successful login page, success.jsp, and the loginfailed/request password page, loginfailed.jsp. When the portlet first displays, you display the landing page. If they log in successfully, you send the to the success page, and if login fails, you send them to the loginfailed.jsp page. That alleviates the need to have portlets displayed and removed from the page.
For some tutorials on portlet development with JSR168, check out my free tutorials: Free Multimedia Tutorials on Portlet Development
Please write back and tell me how this does or not fit into your current scenario.