I don't quite understand your question. Once you have set up your Slingbox to a TV signal provider (such as a cable box) and you have the SB connected via an Ethernet cable (preferred) or wireless to your router, then you can watch the programs on any compatible computer, via the standalone Slingplayer software or an internet browser window (in IE, Firefox, or Chrome). You don't need to designate a "primary" computer, and you can certainly log in to your administrator account from any computer using your administrator login ID and password.
More than one computer can certainly be logged in to the administrator account at a time, but only one computer can be viewing the Slingbox stream at a time, or else you get an error message about someone else is viewing and do you wish to knock them off -- I assume this message appears only if you are logging in via the administrator account and that if you are logging in via a guest account, then you are not provided the option to knock off the other person viewing your stream.
If what you are asking is that you want to be able to view your SB stream on another computer that you will be taking abroad, then you only need to install the Slingplayer standalone application to that computer and log in to your account, or open IE, Firefox, or Chrome and go to http://watch.slingbox.com, log in to your administrator account, and install the Slingplayer add-on when prompted.