@Rosemary10,
You titled this thread "How do I get my husband to grow up and stop being childish?"
Stop giving in to his childish behavior. Stop walking on eggshells around this petulant bully, afraid he will throw a temper tantrum. Stop letting him set the tone for your household.
Adults do not throw temper tantrums. Adults do not walk out when they don't get their way. Adults do not leave their children wondering what they might have done to cause their father to leave. Adults put the family's needs ahead of their own feelings. Adults own up to their failings and ask for forgiveness.
So start treating him like an adult. Stop withholding important information from him. His reaction is his responsibility, not yours. If he is not there when decisions need to be made, make them without him. Keep the household as stable and drama-free as possible for the children. And when they ask why Dad left, tell them the truth. Tell them their father is angry about something, and they can ask him. Call him, hand them the phone, and let him explain himself to his children. If he complains to you, refuse to listen to it.
Ask him what he thinks he is teaching his children by his behavior...that it is OK to run away when they get mad?...that they are not responsible for their behavior when they're angry -- they can always blame someone else?...that it's OK to constantly criticize people they live with?...that it's OK to hurt people's feelings and not apologize? (I could go on.)
The lessons he is teaching his children will come back to haunt him. I guarantee it. Meanwhile, you must be the adult. And that includes treating your husband like an adult, and not letting him get away with ruining your life and the lives of your children.
Good Luck. I mean it.