Rejection of a job offer in favor of another. Is it worth trying to fight back for the first one?
It could never hurt to contact job #1. Maybe they will still need you. I would recommend that you avoid telling them that you are only applying to them because another job rejected you. People do not like being the fallback plan. Simply explain that with more time to consider your options, you came to realize that Job #1 is an excellent opportunity and that the move/distance from you current location should not be a barrier to pursing the important opportunity with #1. 

Understand, of course, that they may have already filled the position with someone else. In that case, all you can do is move on.

p.s. Never deal with people who renege on agreed to terms of employment. That should never be tolerated.