I would compile a list of children's books that have tackled some heavier issues. That way you can see how they are succeeding or failing in their execution, and it will serve as a jumping off point for your own writing.
A couple of books I can recommend -
For younger kids, "The Bad Seed" by Jory John. It's about how you can act out and label yourself as a bad person when bad circumstance happen, but you can heal and change and have a better life.
For middle school kids, "Lois Undercover"by Fanny Brit. A short graphic novel that deals with divorce and an alcoholic father.