One thing I've learned as a children's illustrator is being sensitive to your work being age appropriate to the project you are working on. A cute bear you draw might be fitting for a kindergarten book but it might look too young for a 2nd grade book, and vice versa. And of course, you'll need to be able to draw children at different age levels.
For example, here is an initial sketch I did for a math book:
Comment received: too young looking. To make it for a slightly older audience, I've stylized the animals even more, making them less round, the eyes a bit bigger:
The color palette is important to the age appropriate-ness too. For this, I stayed away from my usual color choices and use a more "sophisticated" palette than I am use to:
I hope this is helpful to you as I always love to see someone's behind the scene process. This is something I've picked up along the way as a children's illustrator and was amazed (and surprised) with the intricacies that come along with doing art for children. And I love it!