Well...the first thing I have to say about that question is this: I'm unable to speak for every published children's author, so I can only talk about the things that interest me!
When I'm not writing, answering phones or emails, here's a list of the things that grab my attention because I consider myself to be a writer by day and a Muay Thai Martial Artist by night...LOL! And now, on to that list (not in alphabetical or necessarily in order of importance because each one is important and has its own merits):
1) Practicing at the Muay Thai martial arts club where I'm involved in Muay Thai, Thai Boxing, Kickboxing, and weightlifting; all of these help me to keep my health and wellness up by making great strength and conditioning goals for all levels - from the physical, emotional, mental and of course, including the spiritual level;
2) I love to watch funny or inspiring movies with my Mom during any holiday;
3) Writing gratitude lists every day - at least five to seven things that I am truly grateful for; an attitude of gratitude goes a very long way!;
4) I really enjoy taking long walks or drives with my Dad. Sometimes, we meet new people in community when we go to play darts or when I play 8-ball or 9-ball billiards; all are great interactive games;
5) I continue my personal development training in various areas - which may involve taking frequent trips to my local library so that I can gather up books on any particular interest because I truly enjoy learning all kinds of things in life!;
6) Getting artistically creative through relaxing with an art called diamond 3D paintings, which are very sparkly and beautiful, having all kinds of designs available;
7) And I love playing Lakota Native Flute, the harmonica, and native hand-frame drum, especially while being at the Sacred Fire. :) :)
This is only a small list of extracurricular activities aside from writing. And every other children's author, I'm fairly certain, would have their own things to delightfully absorb their attention when not crafting some entertaining story.