Re: THE SIMS 3 (SHARING DLC WITH SISTER) 2 DIFFERENT BASE GAME COPIES THOUGH

@Badutiful  No, if you download a base game from one account, you can then only play with expansion and stuff packs that are also owned by that account.  Even if you could trick Origin into downloading and installing your packs along with your sister's base game, which shouldn't be possible anyway, Origin itself would block your sister from using those packs.  Every time Sims 3 is launched through Origin, it checks whether the installed packs are valid on the active account and blocks them if they're not.

All Sims 3 expansions are currently 50% off in Origin right now (through June 20 at 10 am Pacific/1800 GMT), in case you're interested.  I know it's not the solution you're looking for, but it might help a bit.