@littlelambsie I've moved your post to the Sims 3 PC tech section.
It sounds like the file into which the Tiki set is being installed is corrupt, and that's why the content keeps disappearing. It's simple enough to fix though. First, open the launcher and uninstall the Tiki set(s), if you still see them there. Next, close the launcher and move your entire Sims 3 game folder (the one in Documents\Electronic Arts) to the desktop. Open the launcher again to generate a clean folder, and download and install the Tiki set into this folder.
Now you'll have a file called dcdb0.ebc (that's a zero) in DCCache inside your new Sims 3 game folder. Go into DCCache inside your old game folder and look at the numbers on the .ebc files. (You can ignore the .dbc files, which are for third-party custom content.) The .ebc files will be numbered sequentially starting from zero, so you'll need to rename the new .ebc file so that it's one higher than the highest in your old game folder. For example, if your old folder has dcdb0 through dcdb4, the new one will need to be dcdb5.ebc.
Once you've renamed it, move the new file into DCCache inside the old game folder, trash the new game folder you just created, and put the old one back in Documents\EA. For good measure, delete the five cache files inside your game folder as well. They should be deleted any time you add or remove content to your game. For reference, these files are:
