This phase II trial studies how well combination chemotherapy works in treating patients with newly diagnosed stage II-IV diffuse anaplastic Wilms tumors (DAWT) or favorable histology Wilms tumors (FHWT) that have come back (relapsed). Drugs used in chemotherapy regimens such as UH-3 (vincristine, doxorubicin, cyclophosphamide, carboplatin, etoposide, and irinotecan) and ICE/Cyclo/Topo (ifosfamide, carboplatin, etoposide, cyclophosphamide, and topotecan) work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. This trial may help doctors find out what effects, good and/or bad, regimen UH-3 has on patients with newly diagnosed DAWT and standard risk relapsed FHWT (those treated with only 2 drugs for the initial WT) and regimen ICE/Cyclo/Topo has on patients with high and very high risk relapsed FHWT (those treated with 3 or more drugs for the initial WT).