So, I tried sending one of my sims to the secret lot for the cuisine hobby (Sally's Kitchen? Something like that?) Anyway, they would walk to the edge of the lot, but then instead of leaving, they would.. turn invisible. But, it was more like they'd totally disappear, leaving only their plumbob b/c the sims would be unclickable, even in buy mode w/ move_objects on. The sim would still be able to function normally, whether through free will or from me directing it.

Has this ever happened to anyone else? I'm pretty sure it's not because of a hack, though, because I removed all of mine before installing. So, I'm not really sure what the problem is. Does anyone know? :\

If you have hacks in your game (whether or not they were in your DL folder when installing), it sounds like a hack conflict problem. If you have no hacks whatsoever in your game, then it sounds like a tech problem.

Do you have any hacks in your game right now?

I've had that happen in one of my Uni lots. There were 4 sims living there and when I first entered after installing Free Time one of my sims was completely invisable and behaved exactly how you said, I could direct her to do things but couldn't click on her. I have absolutely no hacks but she was loaded with CC.
She went to class and came back visable thank goodness