Dental caries is the disease process that creates cavities in the teeth. As you have described, the first sign of this disease is white spots, usually along the gum line.

Caries depends on sugar in the diet – which you have clearly tried hard to limit and control. Caries also is counteracted by the presence of fluoride.

So, the next thing to do is to increase the frequency that fluoride is available to the teeth. This can be done by applying a very small film of fluoride (prescription strength would be best) directly onto the white spots. Using your finger, rub the fluoride onto the affected areas two or three times a day. Keep up your regular brushing.

It's not the amount of fluoride that makes a difference – it's the frequency that it's made available to the teeth. Too much fluoride can affect the permanent teeth that are forming below the gums.

Because your young child is clearly so good at making cavities, a customized schedule for applying fluoride, arranged in consultation with your child's dentist, would be the next best step.