Chemotherapy and Donor Stem Transplant for the Treatment of Patients With High Grade Brain Cancer

Inclusion Criteria: * Pathological criteria for any high grade primary or recurrent malignant brain tumor - medulloblastoma (patients who are ineligible for tandem autologous transplants or who are at least 3 months post autologous HCT), primitive neuroectodermal tumor (PNET), atypical teratoid rhabdoid tumor (ATRT), malignant glioma, CNS germ cell tumor, intracranial sarcomas, choroid plexus carcinoma, anaplastic ependymoma. High grade tumors defined as those that are grade III or higher based on World Health Organization (WHO) classification grading system or for medulloblastoma: group 3 and 4 molecular subtypes * Patients have to be in at least, a chemo-responsive disease status * Available suitable HCT donor * Creatinine clearance or glomerular filtration rate (GFR) \>= 50 ml/min/1.73m\^2, and not requiring dialysis * Diffusion capacity of the lung for carbon monoxide (DLCO) (corrected for hemoglobin) \>= 50% predicted. If unable to perform pulmonary function tests, then O2 saturation \>= 92% in room air * Bilirubin =\< 3x upper limit of normal (ULN) (with the exception of isolated hyperbilirubinemia due to Gilbert's syndrome) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 5x for age * DONOR: HCT will be done using stem cell sources in the following order of preference (and fulfilling minimal cell dose requirements per institutional standards): * Matched related donor bone marrow (10 of 10 human leukocyte antigen \[HLA\] 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 refused by guardian/donor * Matched allogeneic umbilical cord blood: related * High-resolution matching at A,B, DRB1 (minimum 4/6) * Killer-cell immunoglobulin-like receptor (KIR) major histocompatibility complex (MHC) class 1 preferential mismatch (minimum 4/6) * Matched allogeneic umbilical cord blood: unrelated * High-resolution matching at A,B, DRB1(minimum 4/6) * KIR MHC class 1 preferential mismatch (minimum 4/6) Exclusion Criteria: * Lack of histocompatible suitable graft source * End-organ failure that precludes the ability to tolerate the transplant procedure, including conditioning regimen * Renal failure requiring dialysis * Congenital heart disease resulting in congestive heart failure * Ventilatory failure: requires invasive mechanical ventilation * Human immunodeficiency virus (HIV) infection * Uncontrolled bacterial, viral, or fungal infections * A female of reproductive potential who is pregnant, planning to become pregnant during the study, or is nursing a child * Any patient who does not fulfill inclusion criteria listed above