@Miomidon Store content is encrypted, so it can't be shared between accounts.
Of course you need to use the launcher to install store content, but again, it's not normal for the launcher to require you to login. Have you tried downloading into a clean user data folder yet? Move your entire Sims 3 folder out of Documents\Electronic Arts and onto your desktop, open the launcher to spawn a clean folder, then try to download something.
If this doesn't help, is it possible that the copy of the Sims 3 base game, specifically the product key, is different in your store account than it is in your Origin account? Like I mentioned, store content is encrypted, and it may be checking the product key tied to the installed game with the one on file in the store account.