I'm reading The Mommy Brain: How Motherhood Makes Us Smarter, by Katherine Ellison. One of the later chapters deals with the transferable skills developed in parenting. She mentions time management, dependability, leadership, care-giving, and conflict resolution. The skills she mentions are applicable to most jobs. I think there are also some skills specifically applicable to management positions. Two in particular come to mind:
1. The ability to get things done despite constant interruptions.
Any mother and any manager can tell you that constant interruptions are a hallmark of their jobs. To be successful at either, you have to learn how to get things done- even complex things- while subject to interruption at any time. I don't think this is a skill that can really be taught. Different people will have different methods based on their other strengths and weaknesses.
2. The ability to make decisions with incomplete information.
Both mothers and managers often have to make important decisions based on the information at hand, whether or not that information is complete. In either job, insisting on a complete analysis of every decision would be disastrous. Sometimes the missing information is just not available. Sometimes the time it would take to do the full analysis would result in an undesirable outcome, even if the eventual decision reached was the "right" one. However, both mother and managers also have to know when to say that the information is too incomplete to allow a decision, and take more time to go search for the necessary information. In my experience, the confidence in your ability to recognize which situations can be handled with a decision based on incomplete information comes from practice. I've gotten better at this with more time managing and with more time mommying.
I'm sure there are more transferable skills. Feel free to add some in the comments. I'll keep thinking about this topic and will probably revisit it in the future.