If you put the working catalog on the USB drive you wouldn't have to do any exporting of the catalog. Just move the USB drive from one computer to the other and use the same catalog. Personally, I don't like the idea of just having "finished" images available. If you decide that you want to make you change at some point in the future you either have to make the change to the finished image or go back to the master image and make the change and then export the finished one again. By just maintaining the master images, I can export copies when they are needed for e-mail or other purposes. But after that exported copy has been used it can be discarded.
That's exactly what I want to do but for some reason can't get it right. What do I need to copy from the current HD to the USB3?
Do I copy all of the images and all of the adobe folders? I know it shouldn't be that hard but for some reason I don't have the correct data/file/folders on my USB3.
There is a Lightroom folder inside of the Pictures folder on your computer. That Lightroom folder contains your catalog and your preview images. If you copy that Lightroom folder to the EHD and then open that folder and double-click on the catalog file Lightroom should start and load the catalog from its new location. I don't know if you already have the images on the EHD. You might have to spend little time relinking your image files. Let us know if you need more help.
I will copy all of the images to the EHD then the Lr folder and take it from there.