Do you have Firefox remember to use the launcher for all downloads?
What I did last time I had an issue with Firefox was to clear out all the caches which can be done through Tools > Clear Recent History... I would suggest cache and cookies. Then I went into the preferences (command + ,) > Applications and removed all the ones that involved thesims3.com or the launcher.
Next step would be to open your launcher as well as the TS3 Store. Go into your purchase history (you'll have to use password again) and then try to download. You'll get asked what application to use. I always choose the showtime one but I never check the "remember my choice for sims3 links" so every time I sign into the website it asks. This way I can always choose the latest expansion or stuff pack that I have. It should then load to your already open launcher.
