Maybe the game prefers that you install expansions in the order that they were released. Try uninstalling Sims 3 completely, but make a backup of the saved game folder somewhere in "My Documents" folder. You don't want to accidentally delete your saved games.
Re-install Sims 3 and all your expansion packs in chronological order based on when they are released. Therefore, based what you currently have you should...
1. Install Sims 3
2. Install Late Night
3. Install Pets