What is the difference between these two examples?
Please give me some other example to illustrate the difference.
子供を本を読ませる is ungrammatical, and you have to say 子供に本を読ませる.
Here are the basic rules for causation:
In your question, 読む is a fairly simple transitive verb which takes an object marked with を. So the agent (子供) must be marked with に.
And you can find some edge cases in this question.