I encourage you to keep what I'm about to say in mind. What I'm about to say applies to many people, with various goals, such as losing weight and improving health, but it's rarely talked about. It's the reason overweight people find it hard long term to stick to an improved diet, even though overweight people have the best willpower in the world.
Overweight people exercise their willpower regularly and will slip up and eat the wrong food, from time to time, when they can't resist cravings. They can slip up as a result of additional stresses, emotional challenges or simply willpower burning out.
The gut is the most significant signal to our brain to drive us to eat. There are at least ten times more microbes in our gut than human cells. If your gut ecosystem has developed sugar, pasta and chicken nugget loving bacteria, you have trillions of microbes screaming for more. This is a big signal to eat more bad food.
This can even lead to kid's not even wanting to try new food. Why would they? Their body is signally so strongly to eat the foods that the bad bugs want. If their bacteria a nd yeasts in their gut want processed carbs, that's the signal our kids are getting.
The good news is that if you spend a few days being strict on their eating, not caring so much if they eat less food, but focussing on more nutrients, it will get easier. Their gut ecosystem will improve, and the craving signals will reduce. Once the cravings diminish, it will be easier to widen their diet to more nutrient-dense foods.