Challenging. Your job requires you to adjust frequently to different light patterns and you simply can't do that easily. Early morning light where you are is important, limit alcohol intake and try to get on the schedule of where you are quickly will help. A medication called rozerem (ramelteon) is effective at resetting your internal clock more quickly, but requires a prescription and instructions on how to use it.
Split the difference. Switching time zones every week is very difficult to manage. One solution is to live as if you are in a middle time zone, it will be much easier on your body. Another idea is to live on each coast for longer periods of time, this will minimize the number of times you need to switch your internal clock.