T-Cell Depleted Double UCB for Refractory AML

Inclusion Criteria: * Aged 2 to 45 years with acute myeloid leukemia (AML) 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 AML with low disease burden: For patients \>21 through 45 years of age: must have \<30% marrow blasts within 14 days of enrollment and be at least 28 days from the start of last therapy. For patients 2 through ≤ 21 years of age: must have \>5% marrow blasts after no more than 3 induction attempts. 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 study registration defined as: * Renal: creatinine ≤ 2.0 mg/dL (adult patients) or calculated creatinine clearance \> 40 ml/min (pediatric patients) * Hepatic: bilirubin, aspartate aminotransferase (AST), alanine aminotransferase (ALT), alkaline phosphatase (ALP) ≤ 5 times upper limit of normal * Pulmonary function: diffusing lung capacity for carbon monoxide corrected for hemoglobin (DLCOcorr) \> 50% of normal, (oxygen saturation \[\>92%\] can be used in child where pulmonary function tests (PFT's) cannot be obtained) * Cardiac: left ventricular ejection fraction ≥ 45% * Karnofsky Performance Status ≥ 70% (≥ 16 years) or Lansky Play Score ≥ 50 (pediatrics \< 16 years) * Women of childbearing potential must agree to use adequate contraception (diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, subcutaneous implants, or abstinence, etc.) for the duration of treatment. * All patients will be questioned about prior exposure to antibody therapy (including OKT3, rituximab, trastuzumab, and gemtuzumab) without affect to eligibility. Patients with prior exposure will have a blood sample collected for human antimouse antibody (HAMA). For patients with no prior antibody therapy exposure, no further action will be taken. * Voluntary written consent Exclusion Criteria: * Active infection at time of enrollment or documented fungal infection within 3 months unless clearance from Infectious Disease * Evidence of HIV infection or known HIV positive serology * Pregnant or breast feeding. * If \< or = 21 years old, prior myeloablative transplant within the last 6 months. If \> 21 years old prior myeloablative allotransplant or autologous transplant - if prior conditioning regimen included total body irradiation (TBI), then busulfan/cyclophosphamide(BU/CY) prep should be used * If \> 21 years old - extensive prior therapy including \> 12 months of any alkylator chemotherapy (etoposide \>100 mg/m\^2 x 5 days, cyclophosphamide \>1 gm/m\^2 or mitoxantrone \>8 gm/m\^2) delivered at 3-4 week intervals or \> 6 months alkylator therapy (as above) with extensive radiation (determined by Radiation Oncology, e.g. mantle irradiation for Hodgkin's) and/or prior radiation therapy that makes a patient ineligible for TBI. * Known hypersensitivity to any of the study agents