I'm getting down to the wire about why this is happening. When I did have the mods installed one of them corrupted my save games (except for the one I mentioned earlier). This made me think that an EA script error was the cause because the issue was still there when I uninstalled all mods, cleared caches, etc. I think it's a mod that lets your Sims pack their things before moving out of a household. I never would have suspected it, because it worked with all patches (except for the most recent one, obviously). Luckily, all my saves have multiple backups. Therefore, I was able to recover my save games.
I will give another update when I'm done testing.
Update: I've found the culprit that bugged the heck out of my game. Thank you all so much for your help. If there is anyway I can help, feel free to PM or tag me.
