You could try registering your sims 3 game on thesims3.com which will put it into your origin account, and then download them both via origin. It shouldn't delete your sims or anything, I moved from steam sims to origin sims with no loss of anything. What do you mean a problem updating?
I downloaded world adventures from origin and I have the Sims 3 game on disk & when I try to update the game it would disappear and a day later it not updated
try to manually patch here with the superpatch
http://answers.ea.com/t5/The-Sims-3/FAQ-Current-Patch-1-57-Manual-links-and-more/m-p/67858/highlight
and if you need to contact CS about your missing game here's how to contact CS
They can be found here: https://help.ea.com/contact-us
Choose a category, a game and a platform for the contact options to show up.
If live chat is gray, change your country to US and make sure you're on US Business hours. It might also gray because they're very busy. Try later.
See this post if you have trouble with the site: http://sims3.crinrict.com/en/2012/10/how-to-contact-ea.html
