I was wondering if anybody had thoughts on these questions... for the first question I was contemplating describing a complicated family situation and the stuff I learned from it.... Would a professional story be a better idea?? How about a story about how one of my colleagues was about to be fired and I found out about it before he did and how I tried to subtly convince him to mend his ways and how I talked to mgmt to reconsider? Lot of interesting lessons in this one....
I like the family one more if you can easily transfer the lessons to your work life. That said, if you have time, try writing them both and asking around.
No matter what advice you get from this forum, I don't think there is any substitute from writing the essay the way you envision it and getting feedback from someone who quasi knows you (sibling's friend, co-worker from another department, parent's friend).