This phase II trial study has a 6-patient feasibility portion studying the tolerability of chemotherapy with vincristine sulfate together with topotecan hydrochloride, cyclophosphamide, and bevacizumab in treating young patients with refractory or first recurrent extracranial Ewing's sarcoma. If the therapy is considered tolerable, this feasibility run-in will be followed by a randomized phase II portion studying giving vincristine sulfate together with topotecan hydrochloride, and cyclophosphamide to see how well it works compared with giving vincristine sulfate together with topotecan hydrochloride, cyclophosphamide, and bevacizumab in treating young patients with refractory or first recurrent extracranial Ewing's sarcoma. Drugs used in chemotherapy, such as vincristine sulfate, topotecan hydrochloride, and cyclophosphamide, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Monoclonal antibodies, such as bevacizumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Bevacizumab may also stop tumor growth by blocking blood flow to the tumor. Giving combination chemotherapy together with bevacizumab may kill more tumor cells.