You are not alone! My adults can't go to work, and the kids can't go to school. I get the messages that they will have to leave in an hour, and it appears in their que when it's time. However, when it come up for them to actually do, they are reset, and the "go to work/school" is removed. I have tried clicking on the go-to-work/school button on the employment tab as well as clicking on the sim and telling them to go with the same results.
I've tried everything you have on your list. I also did these things:
- Reset sims.
- Travel - They were able to, but it wouldn't give the option for everyone in the home to go.
- Move - Moved to a different home but still not able to leave.
- New game - Fresh start, got a job, played until it was time to go to work, no-go.
Like your experience, I finally realized that removing the mods fixed the problem. It's only the mods that are causing the issues, not any of my custom content. I'm sure it has to do with the changes that were made with the patch (it's quite a long list of things that were fixed, changed, or tweeked). I'm sure that our mod creators will be working to fix compatibility issues in the next few days/weeks. Until then, I guess we'll have to play without them.
EDIT - After additional testing, the only mod I had causing a conflict was DrChillgood's Safer Chance Cards (from Mod the Sims). It was the only one that had anything to do with work or school. If you have it too, that may be the culprit.