Natural Killer Cells Before and After Donor Stem Cell Transplant in Treating Patients With Acute Myeloid Leukemia, Myelodysplastic Syndrome, or Chronic Myelogenous Leukemia

Inclusion Criteria: * Eligibility for pediatric patients will be determined in conjunction with an MD Anderson Cancer Center (MDACC) pediatrician; patients age 2-17 years old may be enrolled after at least 4 adults (ages 18-65 years old) have been treated without toxicity * Patient with no matched related donor who has a related haploidentical donor identified (=\< 7/8 allele match at the A, B, C, DR loci) who is willing to undergo a bone marrow harvest and an NK cell collection approximately 2 weeks of the recipient's admission for transplant; the donor must be 16 years of age or older and weigh at least 110 pounds * Patients with one of the following diseases: acute myeloid leukemia (AML): a. first complete remission with high-risk features defined as: (i) greater than 1 cycle of induction therapy required to achieve remission; (ii) preceding myelodysplastic syndrome (MDS); (iii) presence of FLT3 mutations or internal tandem duplication or other mutations associated with poor-risk AML (e.g. DNMT3A, TET2); (iv) French-American-British Classification (FAB) M6 or M7 classification; (v) adverse cytogenetics: -5, deletion (del) 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 or complex karyotype (\> 3 abnormalities); (vi) treatment-related AML, or b. second or greater remission; patients beyond second remission have to be in complete remission (CR) at transplant to be eligible, or c. primary induction failure with partial response to therapy who achieve adequate cytoreduction * Patients with myelodysplastic syndromes (MDS): a. de novo MDS with intermediate or high-risk International Prognostic Scoring System (IPSS) scores; patients with intermediate-1 features should have failed to respond to hypomethylating agent therapy, or b. patients with treatment-related MDS * Chronic myeloid leukemia (CML): a. failed to achieve cytogenetic remission or have cytogenetic relapse after treatment with at least 2 tyrosine kinase inhibitors, or b. accelerated phase or blast phase at any time * Performance score of at least 70% by Karnofsky or 0 to 1 by Eastern Cooperative Oncology Group (ECOG) (age \>= 12 years), or Lansky Play-performance scale of at least 70% or greater (age \< 12 years) * Serum creatinine clearance equal or more than 50 ml/min (calculated with Cockcroft-Gault formula) * Bilirubin equal or less than 1.5 mg/dl except for Gilbert's disease * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) equal or less than 200 IU/ml for adults * Conjugated (direct) bilirubin less than 2 x upper limit of normal * Left ventricular ejection fraction equal or greater than 40% * Diffusing capacity of the lung for carbon monoxide (DLCO) equal or greater than 50% predicted corrected for hemoglobin; for children =\< 7 years of age who are unable to perform pulmonary function tests (PFT), oxygen saturation \>= 92% on room air by pulse oximetry * Patient or patient's legal representative, parent(s) or guardian should provide written informed consent; assent of a minor if participant's age is at least seven and less than eighteen years Exclusion Criteria: * Human immunodeficiency virus (HIV) positive; active hepatitis B or C * Uncontrolled infections; principal investigator (PI) is the final arbiter of this criterion * Liver cirrhosis * Central nervous system (CNS) involvement within 3 months * Positive pregnancy test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization * Inability to comply with medical therapy or follow-up