Hello again,
Sounds as though something has gone wrong with the Ambitions installation. Unfortunately Origin downloads frequently are corrupted or go wrong, so you may just have been unlucky with that one.
In the "The Sims 3" folder in Applications you will see the shortcut icons for the base game as well as any expansions or stuff packs installed. If you can see the icon for Ambitions there, try right clicking on it and this should give you the option to show the original file. You can move the original files to the trash from there. This may allow you to commence a re-download from Origin. (Many thanks go to Tremayne from TS3 Mac forum for this suggestion.)
I would recommend that you delete and reinstall the Origin client for Mac and make sure it is up-to-date. This will apparently resolve many download problems with Origin. The latest version can be downloaded from here: http://www.dm.origin.com/mac/download
Also, when downloading from Origin, do NOT use the first install icon. Move your cursor over the game cover and click on the information (letter i) and then click on the install button from there.
Are you running anti-virus software or any clean-up applications? If so, disable these, as they might be deleting files that Origin needs!
If the above doesn't work then you may need to also reinstall the game as well as Origin. Make a backup of your downloads/saves or anything else precious first.
When you uninstall TS3 games on your Mac using the uninstaller, the game leaves behind stray files and isn't completely removed from your computer. These files may conflict with future installations. It is best to completely remove them. BluebellFlora's website provides a guide on how to do this:
http://bluebellflora.com/the-sims-3-on-a-mac/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac/
After cleanly uninstalling, install the base game and patch it up to date. If you cannot update via the Launcher, download and apply the latest cumulative manual patch (called the superpatch) for Mac.
Check that your game works properly. Then install any EPs and SPs that you own, in order of release date.
Good luck - hope you get it working!