Phase III trial to determine the effectiveness of combining systemic chemotherapy and subtenon carboplatin with ophthalmic therapy in treating children who have intraocular retinoblastoma. Drugs used in chemotherapy, such as vincristine, carboplatin, and etoposide, work in different ways to stop tumor cells from dividing so they stop growing or die. It is not yet known whether systemic chemotherapy and subtenon (under the conjunctiva of the eye) carboplatin combined with ophthalmic therapy is effective in treating intraocular (within the eyeball) retinoblastoma.