Edit your login module so that you can pass username and password in the url. Then start the tool from something like this: http://yourwebsite.com/login?username=...&password=...
. You can then leave the work to the tool and your webapp, supposing your tool is managing cookies correctly (Xenu has an option for that.)
After reading the cookies section in the Xenu FAQ, I realized it can access IE's cookies, so...you can try login in IE then (while the browser is still running) run Xenu, enabling its cookies.