Donor Natural Killer Cells in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Patients with relapsed or primary refractory AML; patients with relapsed AML after allogeneic stem cell transplantation, including those who have received donor lymphocyte infusions, are eligible if they have no active graft versus host disease (GVHD) and are off immunosuppression * Have a haploidentical family peripheral blood donor selected for best possible killer cell immunoglobulin-like receptor (KIR) reactivity; KIR typing will not be indicated if there is only one haploidentical donor; KIR typing is advised to be done if feasible and does not delay transplant * Karnofsky or Lansky performance scale (PS) greater or equal to 70 * Serum creatinine =\< 2 mg/dl or creatinine clearance greater or equal than 40 cc/min; creatinine for pediatric patients =\< 2 mg/dl or =\< 2 times upper limit of normal for age (whichever is less) * Forced expiratory volume in 1 second (FEV1), forced vital capacity (FVC) and diffusing capacity of the lungs for carbon monoxide (DLCO) \>= 50% of expected, corrected for hemoglobin; for pediatric patients, if unable to perform pulmonary function tests (most children \< 7 years of age), pulse oximetry \>= 92% on room air by pulse oximetry * Total bilirubin =\< 2 mg/dl or =\< 2.5 x upper limit of normal (ULN) for age (unless Gilbert's syndrome) * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 2.5 x ULN for age * Left ventricular ejection fraction \>= 40%; no uncontrolled arrhythmias or uncontrolled symptomatic cardiac disease * Negative serum test to rule out pregnancy within 2 weeks prior to registration in females of childbearing potential (non-childbearing potential defined as premenarchal, greater than one year post-menopausal, or surgically sterilized) * Sexually active males and females of childbearing potential must agree to use a form of contraception considered effective and medically acceptable by the investigator * Negative serology for human immunodeficiency virus (HIV) * DONOR: Donor must be 16 years of age or older and weigh at least 110 pounds * DONOR: Donor must be a human leukocyte antigen (HLA)-haploidentical relative selected for best NK alloreactivity, defined as having a KIR gene present on the donor NK cells for which the relevant HLA haplotype (KIR ligand) is absent in the recipient and present in the donor or selected on the basis of activating KIR gene content * DONOR: Donor must meet standard institutional eligibility and donor certification criteria for therapeutic cell product donation * DONOR: Not be pregnant as defined by negative serum (beta human chorionic gonadotropin \[beta HCG\]) pregnancy test in females of childbearing potential (non-childbearing potential defined as premenarchal, previous surgical sterilization, or postmenopausal for \> 12 months) * DONOR: Evaluation: history and physical examination; laboratory examinations: hematology, electrolytes, chemistry; infectious disease screening and serology; HLA typing; KIR typing will not be indicated if there is only one haploidentical donor; KIR typing is advised to be done if feasible and does not delay transplant Exclusion Criteria: * Congestive heart failure \< 6 months prior to screening * Unstable angina pectoris \< 6 months prior to screening * Myocardial infarction \< 6 months prior to screening * Uncontrolled infection, defined as an infection which has not resolved spontaneously or does not show evidence of significant resolution after initiating appropriate therapy, excluding chronic asymptomatic viral infections (e.g., human papillomavirus \[HPV\], BK virus, hepatitis C virus \[HCV\], etc.)