Donor Peripheral Blood Stem Cell Transplant and Pretargeted Radioimmunotherapy in Treating Patients With High-Risk Advanced Acute Myeloid Leukemia, Acute Lymphoblastic Leukemia, or Myelodysplastic Syndrome

Inclusion Criteria:

* Patients with advanced AML or ALL defined as beyond first remission, primary refractory disease, or evolved from myelodysplastic or myeloproliferative syndromes; or patients with MDS expressed as refractory anemia with excess blasts (RAEB), refractory cytopenia with multilineage dysplasia (RCMD), RCMD with ringed sideroblasts (RCMD-RS), or chronic myelomonocytic leukemia (CMML)
* Patients not in remission must have CD45-expressing leukemic blasts; patients in remission do not require phenotyping and may have leukemia previously documented to be CD45 negative (because in remission patients, virtually all antibody binding is to nonmalignant cells which make up \>= 95% of nucleated cells in the marrow)
* Patients should have a circulating blast count of less than 10,000/mm\^3 (control with hydroxyurea or similar agent is allowed)
* Patients must have an estimated creatinine clearance greater than 50/mL per minute
* Bilirubin \< 2 times the upper limit of normal
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 2 times the upper limit of normal
* Karnofsky score \>= 70 or Eastern Cooperative Oncology Group (ECOG) =\< 2
* Patients must have an expected survival of \> 60 days and must be free of active infection
* Patients must have an human leukocyte antigen (HLA)-identical sibling donor or an HLA-matched unrelated donor who meets standard Seattle Cancer Care Alliance (SCCA) and/or National Marrow Donor Program (NMDP) or other donor center criteria for peripheral blood stem cell (PBSC) donation; related donors should be matched by molecular methods at the intermediate resolution level at HLA-A, B, C, and DRB1 according to Fred Hutchinson Cancer Research Center (FHCRC) Standard Practice Guidelines and to the allele level at DQB1; unrelated donors should be identified using matching criteria that follows the FHCRC standard practice guidelines limiting the study to eligible donors that are allele matched for HLA-A, B, C, DRB1, and DQB1 (Grade 1), and accepting up to one allele mismatch as per standard practice grade 2.1 for HLA-A, B, or C; PBSC is the only permitted stem cell source
* DONOR: Donors must meet HLA matching criteria as well as standard SCCA and/or NMDP, or other donor center criteria for PBSC donation

Exclusion Criteria:

* Circulating human anti-mouse antibody (HAMA) or human anti-streptavidin antibody (HASA)
* Prior radiation to maximally tolerated levels to any critical normal organ
* Patients may not have symptomatic coronary artery disease and may not be on cardiac medications for anti-arrhythmic or inotropic effects
* Patients with the following organ dysfunction:

  * Left ventricular ejection fraction \< 35%
  * Corrected diffusion capacity of the lung for carbon monoxide (DLCO) \< 35% and/or receiving supplemental continuous oxygen
  * Liver abnormalities: fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction as evidenced by prolongation of the prothrombin time, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis, or symptomatic biliary disease
* Patients who are known seropositive for human immunodeficiency virus (HIV)
* Perceived inability to tolerate diagnostic or therapeutic procedures, particularly treatment in radiation isolation
* Active central nervous system (CNS) leukemia
* Women of childbearing potential who are pregnant (beta-human chorionic gonadotropin \[b-HCG\] +) or breast feeding
* Fertile men and women unwilling to use contraceptives during and for 12 months post-transplant
* Patients may not use vitamin supplements containing biotin from the time of 1 week prior to treatment until 1 week after completion of treatment with all PRIT components
* Inability to understand or give an informed consent