Did you know that eight to ten times more nutrients are available from uncooked vegetables than from the same vegetables cooked? The overall nutrient destruction from cooking is estimated to be about 85%. So, instead of boiling or steaming those veggies, make a platter of raw veggies and let your little ones munch away on those.
I often would have a plate of them available before the main meal was ready, so when they wanted to munch on something they would start to fill up on raw fibrous veggies. It never bothered me if they were too full on them to eat the rest of the meal because I thought they had already partaken of the most nutritious part already anyways!!
Eating too much cooked, enzyme-depleted food drains the body's natural store of enzymes that aid our body's digestion. Aim for at least 50% of your daily food intake to be eaten as raw. Then make the rest of your food healthy choices. And if possible, eat the raw foods first before eating cooked foods as they will be providing more digestive enzymes to help you digest the cooked foods following behind.
And don't forget eating cultured foods, such as the fermented veggies. They add lots of digestive enzymes and healthy flora to your gut.