Wow, that is an extraordinarily long time to export 20 minutes of anything. Be sure you have Background Rendering turned off (at all times). If you look at the background tasks before exporting, make sure nothing is being transcoded or analyzed or anything, before exporting. Also, are you editing with the original native media, and if so, what is that format? (What camera did y'all shoot it with)
And be sure all Events and Projects are on the secondary drive, not on the system drive. You want to bump that RAM up to at least 8GB, too. Anything less than 8GB RAM will stress out with FCP X and Motion 5.
As for proxy media, you can't simply copy it from one machine to another. If it's on an external drive (Events and Projects) then moving the drive to the laptop will be just fine. If you've got Events and Projects on an internal drive, you'll have to duplicate the Project to an external drive, and use either the "include events" or "include only used media" options. Don't manually copy things on the Finder level. This can cause issues.
Each Event and Project in FCP X is a database. Each database has a unique ID number. When FCP X constructs these internally, each has it's own ID. If you copy it in the Finder, you end up with multiple Events / Projects that have the same ID number, and FCP X will actually fuss at you about it, and only allow one version to load up at a time.
If this is an existing Project, duplicate is inside the Project Library as I said, targeting your external drive. Then go to the Event that FCP X created on that drive for the media, right click the Event, and chose "Transcode Media" and select Proxy.