Because so many adults suffer from lower back pain, core exercise training is a must to include in an exercise routine which could then alleviate or lower back pain occurrences. I believe it should be done after childbirth as well (however never do any abdominal or core work without knowing what your transverse abs are and how to hold them in!!)
“Since risk factors of LBP (Low Back Pain) are thought to commence during childhood, results of this study suggest that it may be desirable for children and adolescents to perform moderate-to-high intensity dynamic core exercises during physical education warm-up to improve trunk and core muscular endurance.” read more here
Here is some tools to get you started to help your kids improve their core strength:
Fun Core Exercises For Kids!
Core Strength Activities for Preschoolers and Beginners
Core strength and postural control needed for fine motor skills in children
Kid Ab Workout (video)
Winning Core Body Exercises for Kids (video)