The fact that the computer keeps ejecting them makes me think it's something with the disc that's wrong (even if it works on your dad's computer). Even for Mac people, that's not a common glitch/error we experience.
While this isn't a true "solution" to your problem, the best thing would probably be to digitally download the games from Origin, so you don't have to worry about the discs at all. As long as your games are registered, you can download them (for free) from Origin.
--I know you said you did a clean, uninstall, but just in case, these are the instructions for doing on a Mac (read through them to see if you did this):
http://bluebellflora.com/ts3-on-a-mac/how-to-do-a-clean-uninstall-and-reinstall-on-a-mac-2
--Download the Origin client for Macs: http://www.origin.com/download
--If your games are already registered to your Sims account, make sure you are using that email login and password for Origin. Your games will be there under the "my games" tab in the client for you to download. If you never registered your games you can do so through the "redeem a code" option.
--Remember to patch your game if it needs it, before playing.
Hope this helps work around the disc problem.
