Donor Natural Killer Cells and Donor Stem Cell Transplant in Treating Patients With High Risk Myeloid Malignancies

Inclusion Criteria: * Acute myeloid leukemia who fail to achieve complete remission with one course of induction chemotherapy or after relapse; patients must have less than 20% bone marrow or peripheral blood blasts * Acute myeloid leukemia in first remission with any of the following high risk features defined as: * Adverse cytogenetics: -5, deletion (del) 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 or complex karyotype (\> 3 abnormalities) * Preceding myelodysplastic or myeloproliferative syndrome * Presence of high risk molecular abnormalities including FLT3 mutations, DNMT3A, TET2; ras; kit * French-American-British (FAB) monosomy (M)6 or M7 classification * Treatment related acute myeloid leukemia (AML) * Residual cytogenetic or molecular abnormalities * Myelodysplastic syndromes with intermediate, high or very high risk Revised International Prognostic Scoring System (R-IPSS) score, chronic myelomonocytic leukemia (CMML) or therapy related myelodysplastic syndromes (MDS) * Chronic myeloid leukemia (CML) which: * Failed to achieve a cytogenetic remission to tyrosine kinase inhibitor treatment or has a cytogenetic relapse * Has ever been in accelerated phase or blast crisis * Patient must have an identified HLA (A,B,C,DR) compatible related or unrelated donor who is age 16 years of age or older and weighs at least 110 pounds for the stem cell donation * Zubrod performance status 0 to 2 or Karnofsky of at least 60 * Left ventricular ejection fraction \>= 45%; no uncontrolled arrhythmias or uncontrolled symptomatic cardiac disease * Forced expiratory volume in one second (FEV1) \>= 50% of expected, corrected for hemoglobin * Forced vital capacity (FVC) \>= 50% of expected, corrected for hemoglobin * Diffusing capacity of the lung for carbon monoxide (DLCO) \>= 50% of expected, corrected for hemoglobin * Bilirubin =\< 1.5 mg/dl (unless Gilbert's syndrome) * Serum glutamate pyruvate transaminase (SGPT) =\< 200 IU/ml unless related to patient malignancy * Hepatitis B surface antigen negative and hepatitis C antibody negative * No evidence of chronic active hepatitis or cirrhosis * Patients with a history of hepatitis C, but have a negative viral load, are eligible * The protocol chairman will determine the eligibility of patients related to hepatic abnormalities * Serum creatinine \< 1.5 mg% * Patient or patient's legal representative, parent(s) or guardian able to sign informed consent; patients aged 7 to \< 18 to provide assent * Pediatric patients (age 7-18 years) will be entered only after 3 adult patients have been entered without dose limiting toxicity Exclusion Criteria: * Uncontrolled infection, not responding to appropriate antimicrobial agents after seven days of therapy; the protocol principal investigator (PI) is the final arbiter of eligibility * Pleural/pericardial effusion or ascites \> 1 L * Patients who are known to be human immunodeficiency virus (HIV)-seropositive * Pregnancy: positive pregnancy test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization * Women of child bearing potential not willing to use an effective contraceptive measure while on study * Patients who are known to have allergy to mouse proteins