From the perspective of someone who hires on occasion, I'd really not be tempted to re-hire someone wanting their old job back they only left 4 weeks ago, even if they left on a positive note. It just wouldn't feel right, and I wouldn't want the negative atmosphere with any of my colleagues. I'd suggest your wife figure things out and find a new job. Not to mention the hastle it actualy causes when someone wants to leave/advertising and rehiring admin etc.