If the divorce is amicable, there's no reason why the kid couldn't stay with the father for whatever reason. Living in a better school district, or having more free time. If the mother has a job that makes her travel a lot, or has inconvenient hours, and the dad has a steady nine-to-five, for example. She could be a flight attendant or a chef, even a software designer. I know people in software who don't get home before ten PM on a regular basis. She could also be sick, but that comes with its own bucket of angst, and you might want something more mundane.