I hope I can help clarify some of the confusion.
ArcGIS is a family of products that includes ArcView, ArcEditor, and ArcInfo PRODUCTS. All three include the three desktop applications ArcMap, ArcCatalog, ArcToolbox (plus whatever you get from the extensions you have licensed).
There is an ArcGIS desktop install cd for the "floating" or concurrent licensing versions of the three products.
There is also an ArcView 8.1 install cd -- which is really all the same components that you get with the other DESKTOP installation (i.e. no Workstation -- only ArcMap, Catalog, Toolbox) but for the single-use or stand alone version. It is set up to automatically put you through the register single-use ArcView utility. You either can get a registration number from ESRI by email, fax, or get the registration numbers and then type them in by using the Register through the Internet option.
Perhaps this is what they meant by "installing ArcGIS and ArcView on the same machine".
On your laptop you can use the previous "floating" or concurrent license installation of ArcGIS Desktop (whether that be ArcView, ArcEditor, or ArcInfo) and then you can simply put in the ArcView 8.1 cd and run through the Registration process and type in the registration number you received from ESRI (use this opportunity to register the single-use version of any extensions you may also use).
This will register your machine for the single-use version of ArcView. It will see that ArcGIS is already installed and will not install ArcView "on top of" ArcGIS. Use the Desktop Administrator now to switch to the single use version -- and off you go to the hotel.
When you get back to the office & the network, you can use the Desktop Admin to switch back to one of the floating/concurrent licenses to scale up to use ArcEditor or ArcInfo.
Please let me know if you have any other questions.