Origin has now killed 2 of my games and I can't re-install them.

Did you clean out the registery and delete the game installer files ?

Try the suggestion here: http://answers.ea.com/t5/The-Sims-3/Help-Guide-All-in-one-fix-except-hardware-issues-PC-only/m-p/734448#M36281 where it says Delete game installers

This is not for Mac users. Sorry I should have said I own a Mac computer. Still, I would actually prefer a refund for both games at this point.

If you just bought it you can get a refund through this: http://answers.ea.com/t5/Origin/IMPORTANT-Great-Game-Guarantee/td-p/1418236

If it has been longer, get in touch with customer support

Game advisors can be found through live chat.

1. https://help.ea.com/en/contact-us/ 
2. Set your language to US at the bottom
3. Describe your issue with a few words
4. Select Product: The Sims 3
5. Select Category: Billing/Purchasing or Account Management
6. Select Platform: PC
7. Click Find solution
8. Scroll down and click I still need help
9. Click Chat Now to chat with a Game Advisor
   

With Pics here: http://sims3.crinrict.com/en/2012/10/how-to-contact-ea.html