How would I know if my child is not getting the proper vitamins and nutrients?

Diet history/growth. If your child is not growing well that could be one sign or if he/she is a really picky eater. The best way is with a diet history. Even with picky eaters, children can get all the nutrients they need from what they eat. Sometimes labs are needed to check for nutrient deficiencies. Talk with your doctor about this. I bet you will be reassured that all is actually well.