Combination Chemotherapy With or Without Radiation Therapy in Treating Young Patients With Newly Diagnosed Stage III or Stage IV Wilms' Tumor

Inclusion Criteria: * Patients must be less than 30 years of age at the time of diagnosis * Prior to enrollment on AREN0533, all patients must have been enrolled on AREN03B2 for central pathology review. Stage III patients with LOH transferring from AREN0532 may be enrolled on this study. Eligible patients for AREN0533 must be: * Newly diagnosed Stage IV favorable histology Wilms tumor with or without LOH 1p and 16q or * Newly diagnosed Stage III favorable histology Wilms tumor with LOH for 1p and 16q transferring from AREN0532 * Patients with bilateral Wilms tumors (Stage V) are not eligible for AREN0533 and should be directed to AREN0534 * Patients must begin protocol therapy on AREN0533 by Day 14 after surgery or biopsy, unless medically contraindicated * The Karnofsky performance status must be \>= 50 for patients \> 16 years of age and the Lansky performance status must be \>= 50 for patients =\< 16 years of age * Patients cannot have had prior tumor-directed chemotherapy or radiotherapy except for patients transferring from AREN0532 or those treated for emergent issues, as medically indicated * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) for age (must be submitted for central review by Day 7) * Serum glutamic oxaloacetic transaminase (SGOT) aspartate aminotransferase (AST) or serum glutamic pyruvic transaminase (SGPT) alanine aminotransferase (ALT) \< 2.5 x ULN for age (must be submitted for central review by Day 7) * Shortening fraction ≥ 27% by echoc…