Have you already imported the photos into a Lightroom catalog on the while you were travelling? The answer determines what to do next.
If the photos have not been imported; then you simply import them to the catalog, selecting the COPY option and making sure that you select a destination folder on the external drive with your other photos (or any place else that you want the photos to be stored).
If the photos have already been imported to a Lightroom catalog, then you want to open that catalog, then select all the photos and issue the menu command File->Export as Catalog, give the exported catalog a name; then in the main catalog, select File->Import from Another Catalog and point to the catalog you just exported.
I am unsure whether I made myself clear.
I travel a lot and do not directly use my SD card to import the photos into Lightroom. Instead I create folders on my travel external drive and import the photos from the SD into folders I made on the travel drive. What I am hoping to do is connect the travel drive to my computer without Lightroom being opened and COPY the new folders to my Catalog external drive. Once the new folders are successfully transferred to my Catalog external drive, I want to connect the Catalog drive to my computer and open Lightroom. I am hoping I can just click on ADD with the hope that Lightroom is smart enough to scan and find the new folders and to do its thing. If this workflow does not work then I would be happy to hear what will. Again, any insight will be greatly appreciated. Thank you.
Sounds like you have a clear idea of what you want and of how to do it:
Using OS tools (finder or explorer), copy the images off the SD card onto the travel drive using folders of your choosing.
Copy the images from the travel drive to your main external drive, using OS tools (Finder or Explorer).
In LR, import the images on the external drive using the ADD option to keep them where they are.