Vinorelbine Tartrate and Cyclophosphamide in Combination With Bevacizumab or Temsirolimus in Treating Patients With Recurrent or Refractory Rhabdomyosarcoma

Inclusion Criteria: * Diagnosis * Patients with first relapse or progression of rhabdomyosarcoma are eligible * Patients with primary refractory disease are eligible * Primary refractory disease is defined as first progression after receiving at least one course of cyclophosphamide or ifosfamide containing chemotherapy without prior demonstration of a radiographic response to chemotherapy (progression on irinotecan-containing chemotherapy without cyclophosphamide or ifosfamide containing chemotherapy will not be considered a first progression) * Note: Patients without measurable or evaluable disease are eligible * Patients must have had a previous histological verification of rhabdomyosarcoma at original diagnosis * Patients must have a Karnofsky or Lansky performance status score of \>= 50%, corresponding to Eastern Cooperative Oncology Group (ECOG) categories of 0, 1, or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age * Patients must have a life expectancy of \>= 8 weeks * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study * Myelosuppressive chemotherapy: Must not have received within 3 weeks prior to entry onto this study (4 weeks if prior nitrosourea) * Biologic (anti-neoplastic agent): * Patients may have received prior therapy with oral tyrosine kinase inhibitors or other similar agents; at least 7 days must hav…