Changing external drive

First, the simple solution.
You have both external drives plugged in.
You use the organizer to move your pictures folders from one drive to the other. In the left 'Folders' panel in tree view, you see the folders tree of your various drives, internal or internal. You simply click and drag the master folder of the old drive to the root folder of the new drive.
Simple? Yes, but you must be patient since rewriting the files takes a lot of time for a big library and you get not progress bar to see the percentage done. Many users don't trust that solution for fear of a problem during the transfer. In my opinion, those fears are exaggerated. I have had a power failure at 95% of the process... The result was that the process was cancelled and I was back to the start, except I had use the explorer to delete the 95% already moved (copied, as a matter of fact, the originals were not deleted).

Then the 'safe' solution: the classical backup and restore method:
helpx.adobe.com/photoshop-elements/kb/backup-restore-move-catalog-photoshop.html

It may seem much longer, but since such a job requires a full backup to be sure, it's not more trouble and time.

With both solutions, the organizer updates the paths of the files to the new identity of the drive (letter drive and internal serial number).

Now, what about another solution: using a copy or backup external program to move the library folder tree in the same tree structure.
In your catalog, all files are now shown as 'disconnected' or 'missing'. It's possible to use the 'reconnect' function of the organizer, but I bet you'll have difficulties to succed in the task. I don't recommend that solution, but it may be a decent alternative if you only move a branch of your library folder tree.

Other solution after such external software transfer: If you assign the same letter drive to the new one and assign the same internal serial number, no reconnecting will be necessary. That can be done via a clone utility (like Acronis) or by using Windows utilites to re-assign the internal serial number. Warning: after that, don't try to plug in both 'clones' at the same time! Disaster in the catalog!

I also have a personnal solution in two steps: I use Windows Synctoy to sync my library folder to another drive. Much, much more faster than an incremental backup. Then I use an sqlite utility to update the catalog database to the new drive identification.