Since the introduction of patch 1.12 the location of the Mods/Packages folder needs to be changed. EA done this to make the game more compatible with .package files. You will find the information you require to relocate your Mods/Packages folder here. Once you have succeeded in completing this process you may wish to check if the download now installs or just continue on with the next process.
There is a program created by Delphy that converts Sims 3 pack files to .package files. You can get it from here. Once you have it converted and placed in your relocated Mods/Packages folder, and deleted the 4 cache files (Documents/Electronic Arts/Sims 3 [CASPartCache.package][compositorCache.package][scriptCache.package][simCompositorCache.package] your download will show up in your game, although I believe store items will not show up if converted and installed this way.
