211^At-BC8-B10 Before Donor Stem Cell Transplant in Treating Patients With High-Risk Acute Myeloid Leukemia, Acute Lymphoblastic Leukemia, Myelodysplastic Syndrome, or Mixed-Phenotype Acute Leukemia

Inclusion Criteria: * Patients must have AML, ALL, high-risk MDS, or MPAL (also known as biphenotypic) meeting one of the following descriptions: * AML, ALL, or MPAL in first remission with evidence of measurable residual disease (MRD) by flow cytometry * AML, ALL, or MPAL beyond first remission (i.e., having relapsed at least one time after achieving remission in response to a treatment regimen) * AML, ALL, or MPAL representing primary refractory disease (i.e., having failed to achieve remission at any time following one or more prior treatment regimens) * AML evolved from myelodysplastic or myeloproliferative syndromes * MDS expressed as refractory anemia with excess blasts (RAEB) * Chronic myelomonocytic leukemia (CMML) by French-American-British (FAB) criteria * 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 non-malignant cells which make up \>= 95% of nucleated cells in the marrow) * Patients must be \>= 18 and =\< 75 years of age * 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 by the following formula (Cockcroft-Gault); serum creatinine value must be within 28 days prior to registration * Patients must have normal hepatic function (bilirubin within normal limits, aspartate aminotransferase \[AST\] and alanine aminotransferase \[ALT\] \< 2 times the upper limit of normal) within 2 months prior to the astatine-211 infusion date (with the exception of patients that are known to have Gilbert's disease, for whom total bilirubin is allowed up to 3 x upper limit of normal \[ULN\]) * Eastern Cooperative Oncology Group (ECOG) \< 2 or Karnofsky \>= 70 * Patients must be free of uncontrolled infection * Patients with prior non-myeloablative or reduced-intensity conditioning allogeneic-hematopoietic cell transplant (HCT) must have no evidence of ongoing GVHD and be off GVHD treatment immunosuppression for at least 6 weeks at time of enrollment * Patients must have normal elastography * If ferritin is elevated, patient must have less than 7 mg/g liver iron concentration on liver T2\* MRI * Patients should have an official gastrointestinal (GI) consult prior to the transplant for full evaluation * Patients must have an HLA-matched related donor or an HLA-matched unrelated donor who meets standard Fred Hutch and/or National Marrow Donor Program (NMDP) or other donor center criteria for peripheral blood stem cell (PBSC) or bone marrow donation, as follows: * Related donor: related to the patient and genotypically or phenotypically identical for HLA-A, B, C, DRB1 and DQB1; phenotypic identity must be confirmed by high-resolution typing * Unrelated donor: * Matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing; OR * Mismatched for a single allele without antigen mismatching at HLA-A, B, or C as defined by high resolution typing but otherwise matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing * Donors are excluded when preexisting immunoreactivity is identified that would jeopardize donor hematopoietic cell engraftment; the recommended procedure for patients with 10 of 10 HLA allele level (phenotypic) match is to obtain panel reactive antibody (PRA) screens to class I and class II antigens for all patients before HCT; if the PRA shows \> 10% activity, then flow cytometric or B and T cell cytotoxic cross matches should be obtained; the donor should be excluded if any of the cytotoxic cross match assays are positive; for those patients with an HLA Class I allele mismatch, flow cytometric or B and T cell cytotoxic cross matches should be obtained regardless of the PRA results; a positive anti-donor cytotoxic crossmatch is an absolute donor exclusion * Patient and donor pairs homozygous at a mismatched allele in the graft rejection vector are considered a two-allele mismatch, i.e., the patient is A\*0101 and the donor is A\*0102, and this type of mismatch is not allowed Exclusion Criteria: * Patients may not have symptomatic coronary artery disease and may not be on cardiac medications for anti-arrhythmic or inotropic effects * Left ventricular ejection fraction \< 35% * Corrected diffusing capacity of the lungs for carbon monoxide (DLCO) \< 35% or receiving supplemental continuous oxygen; when pulmonary function test (PFT)s cannot be obtained, the 6-minute walk test (6MWT, also known as exercise oximetry) will be used: Any patient with oxygen saturation on room air of \< 89% during a 6MWT will be excluded * 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 to be seropositive for human immunodeficiency virus (HIV) * Perceived inability to tolerate diagnostic or therapeutic procedures * Active central nervous system (CNS) leukemia at time of treatment * Patients with prior myeloablative allogeneic-HCT * Women of childbearing potential who are pregnant (beta-human chorionic gonadotropin positive \[beta-HCG+\] or breast feeding * Fertile men and women unwilling to use contraceptives during and for 12 months post-transplant * Inability to understand or give an informed consent * Allergy to murine-based monoclonal antibodies * Known contraindications to radiotherapy