Induction Therapy Including 131 I-MIBG and Chemotherapy in Treating Patients With Newly Diagnosed High-Risk Neuroblastoma Undergoing Stem Cell Transplant, Radiation Therapy, and Maintenance Therapy With Isotretinoin

Inclusion Criteria: * Patients have a diagnosis of neuroblastoma (International Classification of Diseases for Oncology \[ICD-O\] morphology 9500/3) or ganglioneuroblastoma verified by histology or demonstration of clumps of tumor cells in bone marrow with elevated urinary catecholamine metabolites; patients with the following disease stages at diagnosis are eligible, if they meet the other specified criteria: * Patients with newly diagnosed neuroblastoma with International Neuroblastoma Staging System (INSS) stage 4 are eligible with the following: * v-MYC myelocytomatosis viral related oncogene, neuroblastoma derived (avian) (MYCN) amplification (\> 4-fold increase in MYCN signals as compared to reference signals) and age \>= 365 days regardless of additional biologic features * Age \> 18 months (\> 547 days) regardless of biologic features * Age 12-18 months (365-547 days) with any of the following 3 unfavorable biologic features (MYCN amplification, unfavorable pathology and/or deoxyribonucleic acid \[DNA\] index = 1) or any biologic feature that is indeterminant/unsatisfactory/unknown * Patients with newly diagnosed neuroblastoma with INSS stage 3 are eligible with the following: * MYCN amplification (\> 4-fold increase in MYCN signals as compared to reference signals), and age \>= 365 days, regardless of additional biologic features * Age \> 18 months (\> 547 days) with unfavorable pathology, regardless of MYCN status * Patients with newly diagnosed INSS stage 2a/2b with MYCN amplification (\> 4-fold increase in MYCN signals as compared to reference signals) and age \>= 365 days, regardless of additional biologic features * Patients \>= 365 days initially diagnosed with: INSS stage 1, 2, 4S who progressed to a stage 4 without interval chemotherapy; these patients must have been enrolled on ANBL00B1; it is to be noted that study enrollment must occur within 4 weeks of progression to stage 4 for INSS stage 1, 2, 4S * Patients must have had no prior systemic therapy except for localized emergency radiation to sites of life-threatening or function-threatening disease and/or no more than 1 cycle of chemotherapy per low- or intermediate-risk neuroblastoma therapy (P9641, A3961, ANBL0531) prior to determination of MYCN amplification and histology * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 OR serum creatinine based on age and/or gender as follows: * =\< 0.6 mg/dL (1 to \< 2 years of age) * =\< 0.8 mg/dL (2 to \< 6 years of age) * =\< 1.0 mg/dL (6 to \< 10 years of age) * =\< 1.2 mg/dL (10 to \< 13 years of age) * =\< 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 to \< 16 years of age) * =\< 1.7 mg/dL (male) or 1.4 mg/dL (female) ( \>= 16 years of age) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) or serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 10 x ULN for age * Shortening fraction \>= 27% by echocardiogram or * Ejection fraction \>= 50% by radionuclide evaluation * No known contraindication to peripheral blood stem cell (PBSC) collection; examples of contraindications might be a weight or size less than the collecting institution finds feasible, or a physical condition that would limit the ability of the child to undergo apheresis catheter placement (if necessary) and/or the apheresis procedure * 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 Exclusion Criteria: * Females of childbearing potential must have a negative pregnancy test; patients of childbearing potential must agree to use an effective birth control method * Female patients who are lactating must agree to stop breast-feeding * Patients that are 12-18 months of age with INSS stage 4 and all 3 favorable biologic features (i.e., non-amplified MYCN, favorable pathology, and DNA index \> 1) are not eligible * Patients are not eligible if they have received local radiation which includes any of the following: 1200 centigray (cGy) to more than 33% of both kidneys (patient must have at least 1 kidney that has not exceeded the dose/volume of radiation listed) or 1800 cGy to more than 30% of liver and/or 900 cGy to more than 50% of liver; emergency local irradiation is allowed prior to study entry, provided the patient still meets eligibility criteria