The medical system is a social provision, which means that everyone has health care insurance and access to care. The state also provides regular check-ups for children. The basic system starts with insurance (or 'verzekering') often provided through an employer.
There are many good hospitals in the Netherlands and all can be expected to have a high level of care. Most Dutch hospitals offer the same specializations. However, some do specialize in particular ailments. Your physician can direct you to a suitable one if this is the case. Unless it is an emergency, you will need a referral letter from your GP to go to a hospital in the Netherlands.
Children under 18 do require a basic Dutch health insurance but can be registered free of charge under the (supplementary) policy of one of their parents. Make sure that you register your children with your health insurance provider. Newborns must be registered within 4 months. Children are given basic care and vaccinations through the local child health centre (‘consultatiebureau’) for children under 4 years of age, but in case of illness they should visit a physician.