• Patient aged 0 to 60 years at time of consent
• Relapse more than 100 days after first stem cell transplant
• Diagnosis of acute myelogenous leukemia, acute lymphoblastic leukemia, other acute leukemias, myelodysplastic syndromes, or CMML without myelofibrosis
• Must have received one prior allogeneic stem cell transplantation
• Karnofsky score 70% or higher if age 16 or older, or Lansky score 70% or higher if under 16
• Kidney function with creatinine clearance over 50 ml/min
• Bilirubin less than 2 mg/dL unless benign causes
• ALT less than 5 times upper limit of normal
• Pulmonary function with DLCO 60% or more predicted, or waived if unable to complete test
• Left ventricular ejection fraction over 50%
• Two cord blood units meeting specific HLA match and cell dose criteria, including minimum 3/8 HLA match, cell doses, and cryopreservation standards

History of severe allergic reactions to study medication Currently pregnant or breastfeeding Recent participation in another clinical trial within the last 30 days Presence of uncontrolled medical conditions that could affect safety