When should hubby stop traveling for work?

Okay, I need some advice! My DH travels a lot for work. He promised after this week's trip to NYC, that he'd be done traveling until baby comes. Now his coworker is begging him to fly to KY the week after (we live in CA). My dr told me no traveling after 32 weeks and I'll be just about 33 weeks when this impending trip happens. The closest relatives live over an hour away, so I'm not sure what I'd do if something were to happen. I would hate to go into labor early and be totally alone. Thoughts?