I'm far from an expert on illustrating for children, but here are some things I've found helpful. I'll be adding to this section on a regular basis - so please check back!
Time lends objectivity
You've been sitting there for 5 hours - you're tired, fed up and you still can't quite hit on the right look for your character. Take a break! When you're working closely on any kind of illustration project, it's easy to become blind as to what's really working and what's not.
The time I experience this most is in character design. I have in the past drawn out hundreds of sketches for the same character and eventually not been able to decide which one I should use. But when I get back to my desk the next day, I can easily spot which one I should use.
This applies to all aspects of illustration - from layout, to decisions about colour, to things like perspective and other drawing considerations. Take a break of 24 hours (if the deadline allows) and then come back tomorrow fresh. I guarantee it will be much easier to make those decisions with a fresh eye.