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 ade…