Add your QlikView Server to the Trusted sites in Internet Explorer, and in the Custom Level button, you can set automatic logon using current user name and password. So you will not be prompted for user and password and will let you access the AccessPoint and see only those documents that you have permissions. I'm assuming your section access is using NTNAME instead of USERID.
Any other web browser will ask at least once for username and password, that you must provide in the form DOMAIN\USERNAME. If the browser is configured to remember credentials, you will be prompted only once, and will use this stored credentials for any further connection.
That should work for any web browser. If that does not happen like that, let us know.
Hope that helps.