I found a fantastic resource through a LinkedIn contact, which anyone hoping to work in children's books or publishing should take advantage of. ChildrensIllustrators.com has a whole stockpile of interviews with art directors, publishers, and editors available to view on their website. Unfortunately the interviews are not dated, so I can't say how old these interviews are or if the people interviewed are even in that same position still, but this can be a helpful resource to get a general picture about how to approach an art director or publisher.
The very first interview I read, and connected with, was with Carol Chu as the art director of the children's trade division at Houghton Mifflin Harcourt:
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Interview with Carol Chu*
Some highlights that I found especially useful:
On keeping your focus and going after your goals:
"At every fork in the road, I took the path which eventually led me here."
What she looks for when viewing illustrator submissions:
"The portfolios which get passed around have a distinct voice/vision and we send them around to everyone in the design department. I would rather see a portfolio with a strong point of view which might not be right for a lot of books than a middle-of-the-road functionally competent portfolio which can be forgettable and generic."
On whether she prefers working with established pros or new talent:
"I care about meeting deadlines and clear communication between me and the illustrator... I prefer working with someone whose QUALITY is consistent."