Switch to Desktop 2

If you quit BTT, does the ctrl+2 shortcut then switch to space 2?

No. I forgot to mention that's why I think this a generic Apple bug.

I had previously disabled BTT, but I just exited and ^2 still does nothing (doesn't go to Desktop 1 like I said before... I might have been wrong or that might have been some temporary thing).

Possibly try to delete this file and restart your system:
~/Library/Preferences/com.apple.symbolichotkeys.plist

To delete it you can use this terminal command:
rm ~/Library/Preferences/com.apple.symbolichotkeys.plist

I'm not sure whether that will help, but that's the file were all hotkeys from System Settings => Keyboard => Shortcuts are stored. It automatically gets regenerated when restarting.

DUDE! That did it! You ever come to the Bay Area I will buy you a beer! THANK YOU.

:tada:

such a weird bug!

Agreed! And I've seen some weird ones!! Haha.