By default tomcat will create a session cookie for the current domain.
If you are on www.example.com, your cookie will be created for www.example.com (will only work
I've run into this at $DAYJOB. In my case I wanted to implement SSL signon then redirect to a non SSL page. The core problem in tomcat is the method (from memory) SessionManager.configureSessionCookie which hard codes all the variables you would like to get access to.
I came up with a few ideas, including a particularly egregious hack using mod_headers in apache to rewrite the cookie based on regex substitution.
The definative way to solve this would be to submit a patch to the tomcat developers that adds configurable parameters to the SessionManager class.