This phase III clinical trial is studying how well combination chemotherapy and surgery work in treating young patients with Bilateral Wilms tumor and children who are a special risk for forming tumors in both kidneys. Drugs used in chemotherapy work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. 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.