I want to have the HOME directory of one user on an external drive and the HOME directories of all other users in the usual place.
As the user, or as root, you can use "Users & Groups" settings dialog (search for it using the dash) to accomplish this:
Users & Groups --> Select the user --> Properties --> Advanced --> Home Directory
Note that you must move/copy the data to the external drive manually first, and then use the settings dialog to point it there.
You can also achieve this using usermod on the command line (as root or the user):
usermod --home /path/to/external/drive --move-home USERNAME
where USERNAME is the name of the user whose folder you want to move. Note that --move-home moves the data of the folder for you, so unlike the method using the settings dialog, you will not have to do this yourself.