How long can a vinaigrette last if emulsified with raw egg?
I'd recommend only keeping vinaigrette for 7 days or less (refrigerated, of course). It's not that difficult and you'll be avoiding a lot of quality and safety issues.

Another thing you need to be aware of is that raw garlic can cause botulism, which can result in hospitalization and death. I think close relatives of garlic, such as shallots also contain botulinum spores, as well as honey. If they sit in an anaerobic medium (oxygenless), such as oil in a vinaigrette, they can start to grow and produce deadly toxins.

Also, after a week I feel like fresh ingredients such as herbs will start to go bad. And olive oil can definitely go rancid after 4 weeks!

Discuss your concerns management and if they don't listen then I'd email/call your local health department and I am sure they'd help you make sure everything is safe. Best of luck!