Chemotherapy, Total-Body Irradiation, Donor Natural Killer Cell Infusion, Aldesleukin, and UCB Transplant in Treating Patients With Relapsed or Refractory AML

Inclusion Criteria: * Aged 0 to 45 years who meet one of the following criteria: * Primary induction failure defined as no complete remission (CR) after two or three induction cycles (no blast limit). * Relapsed acute myeloid leukemia (AML) with low disease burden * For patients 19 through 45 years of age: must have less than 10% marrow blasts at time of enrollment for patients who did not receive re-induction or measured at least 28 days from the start of re-induction therapy. Patients who have relapsed more than 12 months following a prior hematopoietic cell transplant (HCT) and did not reach CR following one re-induction cycle but have less than 10% marrow blasts are eligible. * For patients 0 through 18 years of age: must have less than 50% marrow blasts after no more than 3 induction attempts * CR3 or greater. This will include CRp defined as CR without platelet recovery to 100,000/mcL. * CR1 or CR2 with high risk features (therapy induced, prior myelodysplastic syndrome (MDS) or myeloproliferative disease (MPD), high risk cytogenetic or molecular phenotype) with no available alternate (sibling, URD or UCB) donors. * Patients with prior central nervous system (CNS) involvement are eligible provided that it has been treated and is in remission. CNS therapy (chemotherapy or radiation) should continue as medically indicated during the protocol. * Have acceptable organ function within 14 days of enrollment defined as: * Renal: creatinine ≤ 2.0 mg/dL (ad…