A Study to Give Treatment Inside the Eye to Treat Retinoblastoma

Inclusion Criteria: * Patient must be \< 18 years of age at enrollment * Patient must have newly diagnosed intraocular (localized) retinoblastoma and meet one of the following criteria: * Unilateral Group D retinoblastoma with vitreous seeding; OR * Bilateral retinoblastoma with worst eye Group D, with vitreous seeding present and the contralateral eye is Group A-C; OR * Bilateral Group D retinoblastoma with at least one eye with vitreous seeding; OR * Bilateral retinoblastoma with one Group D eye with vitreous seeding and one Group E eye where the Group E eye has been enucleated prior to any therapy. Note exclusion for high-risk features * Bilateral retinoblastoma with one Group D eye with vitreous seeding and one Group E eye where the Group E eye has not been enucleated prior to any therapy at the discretion of the treating physician. Note exclusion for patients with evidence of metastatic or extra orbital spread * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2. Use Karnofsky for patients \> 16 years of age and Lansky for patients =\<16 years of age * Peripheral absolute neutrophil count (ANC) \>= 750/uL (must be performed within 7 days prior to enrollment unless otherwise indicated) * Platelet count \>= 75,000/uL (transfusion independent) (must be performed within 7 days prior to enrollment) * A serum creatinine based on age/sex as follows (must be performed within 7 days prior to enrollment; must be repeated prior to the start of protocol therapy if \> 7 days have elapsed from their most recent prior assessment): * 1 month to \< 6 months = 0.4 (male and female) * 6 months to \< 1 year = 0.5 (male and female) * 1 to \< 2 years = 0.6 (male and female) * 2 to \< 6 years = 0.8 (male and female) * 6 to \< 10 years = 1.0 (male and female) * 10 to \< 13 years = 1.2 (male and female) * 13 to \< 16 years = 1.5 (male) and 1.4 (female) * \>= 16 years = 1.7 (male) and 1.4 (female) OR - a 24-hour urine Creatinine clearance \>= 70 mL/min/1.73 m\^2 OR - a glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2. GFR must be performed using direct measurement with a nuclear blood sampling method OR direct small molecule clearance method (iothalamate or other molecule per institutional standard) * Note: Estimated GFR (eGFR) from serum creatinine, cystatin C or other estimates are not acceptable for determining eligibility * For patients \< 1 month of age, serum creatinine levels must be \< 1.5 x the treating institution's creatinine upper limit of normal (ULN) for patients \< 1 month of age or the creatinine clearance or radioisotope GFR must be \>= 70 mL/min/1.73 m\^2 * The threshold creatinine values were derived from the Schwartz formula for estimating GFR utilizing child length and stature data published by the Center for Disease Control (CDC) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age (must be performed within 7 days prior to enrollment; must be repeated prior to the start of protocol therapy if \> 7 days have elapsed from their most recent prior assessment) * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 135 U/L (must be performed within 7 days prior to enrollment; must be repeated prior to the start of protocol therapy if \> 7 days have elapsed from their most recent prior assessment) * Note: For the purpose of this study, the ULN for SGPT (ALT) has been set to the value of 45 U/L Exclusion Criteria: * Patients with evidence of metastatic or extra-orbital spread * Patients must not have an invasive infection at time of protocol entry * Patients must not have had any prior anti-cancer therapy other than cryotherapy and/or laser therapy (green or infrared) to the study eye(s) and non-study eye, including systemic chemotherapy, intra-arterial chemotherapy, radioactive plaque, brachytherapy, or radiation therapy. * Note: A study eye is defined as being Group D with vitreous seeding. Patients may have had enucleation of one eye as long as the remaining eye is Group D with vitreous seeds * Patients with bilateral disease who undergo enucleation of a Group E eye prior to initiation of therapy and show evidence of high-risk histopathology features in the enucleated eye. High-risk histopathology includes choroid involvement \>= 3 mm, post lamina optic nerve involvement, full thickness scleral invasion or optic nerve invasion to the cut end * Female patients who are pregnant since fetal toxicities and teratogenic effects have been noted for several of the study drugs. A pregnancy test is required for female patients of childbearing potential * Lactating females who plan to breastfeed their infants * Sexually active patients of reproductive potential who have not agreed to use an effective contraceptive method for the duration of their study participation * All patients and/or their parents or legal guardians must sign a written informed consent * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met