Donor Stem Cell Transplant After Chemotherapy for the Treatment of Recurrent or Refractory High-Risk Solid Tumors in Pediatric and Adolescent-Young Adults

Inclusion Criteria: * Pathological criteria, including malignant recurrent/refractory solid tumors. This would include: * Ewing's/peripheral primitive neuroectodermal tumor (PNET) * Malignant peripheral nerve sheath tumor, neurofibrosarcoma * Rhabdomyosarcoma * Neuroblastoma (patients who are ineligible for tandem autologous transplant or who are at least 3 months post autologous HCT) * Desmoplastic small round cell tumor (DSRCT)- both new diagnoses as well as recurrent/refractory disease * Patients must have chemo-responsive disease, defined as; 30% or greater decrease in the tumor target lesions when compared to its pre-treatment evaluation. Patients with complete response will be eligible to participate * Available suitable HCT donor * Creatinine clearance or glomerular filtration rate (GFR) \>= 50 ml/min/1.73m\^2, and not requiring dialysis * Diffusing capacity of lung for carbon monoxide (DLCO) (corrected for hemoglobin) \>= 50% predicted. If unable to perform pulmonary function tests, then oxygen (O2) saturation \>= 92% in room air * Bilirubin =\< 3 x upper limit of normal (ULN) and alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 5 x for age (with the exception of isolated hyperbilirubinemia due to Gilbert's syndrome) * DONOR: Matched related donor bone marrow (10 of 10 HLA alleles \[HLA-A, B, C, DR, and DQ\]. Matched related donor peripheral blood stem cell (PBSC) is allowed only if collection of bone marrow (BM) is not available or …