Extremely difficult problem. Movement of the eye is called "nystagmus". The child needs to be in a tertiary pediatric ophthalmology referral center like a medical school. Needs a team of ophthalmologists including pediatric ophthalmologists, retina specialists and perhaps even glaucoma specialist. Many visits will be required to you want a center that your can drive or fly to in a reasonable amount of time and money. Very important to check left eye to make sure it doesn't have congential abnormalities also. Nystagmus often indicates poor vision in the better eye also. Sorry a huge challenge even with modern treatment.