This phase III trial studies how well combination chemotherapy and surgery work in treating young patients with Wilms tumor. Drugs used in chemotherapy 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. Giving more than one drug (combination chemotherapy) may kill more tumor cells. Giving combination chemotherapy before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed. Giving it after surgery may kill any tumor cells that remain after surgery.