Do yourself a favor, put ALL of the photos on the external HD. Don't put photos any more on the SSD, they don't belong there, it's too small anyway, and any possible speed improvement by putting photos on the SSD is so trivial that you will never notice it. Your SSD should contain the Lightroom catalog and previews (but not the photos), and of course any software you want to put there.
Do not split catalogs. This is an idea that ought to never cross your mind. To me, this is one of the worst things you could possibly do, I think this is a horrible idea.
So what should you do? In your operating system, you want to COPY (not MOVE), all the photos on the SSD to the external HD, keeping the folder hierarchy unchanged. Then in Lightroom, direct Lightroom to look at the new location of the photos, by following the instructions in the section entitled "Part 2 — Updating Folder Location" of this document; then once everything is working properly, you can delete the photos from the SSD. Since you say you won't have the external HD plugged in all the time, you could create smart previews of the photos you want to work on (while the external HD is connected), this will allow you to work on the photos in Lightroom even if the photos are on the external HD which is not plugged in. This does take up space on your SSD, but not nearly as much space as the actual photos.
Thank you very much for the answer. That is a great idea.
I'll get on that right away.
Thank you again for answering so quickly.