@stephieeepants Do you want the game's program files on the external hard drive, or are you only trying to transfer your user data (saves, saved households and builds, mods and custom content) back and forth? If this is only about the user content, the easiest thing is probably to manually copy the relevant files back and forth between your two computers, using the external hard drive.
Normally, Sims 4 looks for user data in Documents\Electronic Arts\The Sims 4 and reads whatever's inside. Since you're already using an external drive, it would be easy to copy a save, or the entire saves folder, from one computer to the other. You could also transfer mods and custom content this way.
Another approach would be to store your user data folder on the external and create a symbolic link to it on each computer. The advantage of this is that you wouldn't have to copy any files; you'd just plug in the external, make sure it was recognized, and pick up where you left off. However, depending on the type of connection the hard drive uses and the speed of the internal hard drive on each computer, the game may load much more slowly with your user data on the external. This might not be noticeable if you only have a small amount of cc, but once you get into the range of several GB, it may make enough of a difference to be inconvenient.
If you do want to try using a symbolic link, be sure to make backups of any content you'd be upset to lose.
If you want to store the program files on the external as well, that shouldn't be as much of an issue, and it sounds like you may have already figured this part out. Let me know if you do in fact need help with it.
