Donor Peripheral Stem Cell Transplant and Donor Natural Killer Cell Transplant After Total-Body Irradiation, Thiotepa, Fludarabine, and Muromonab-CD3 in Treating Patients With Leukemia or Other Blood Diseases

OBJECTIVES: Primary * Determine the effect of haploidentical donor CD34+ purified peripheral blood stem cells and donor natural killer (NK) cells on the risk of developing grades III-IV acute graft-vs-host disease in patients with leukemia or other hematologic diseases. Secondary * Determine the risk for mortality from infection before day 180 in patients treated with this regimen. * Determine the risk for graft rejection in patients treated with this regimen. * Determine the risk for life-threatening infections in patients treated with this regimen. * Determine the concentration of subsets of NK, NK-T, T cells, and dendritic cells in the CD34+ NK/NK-T-enriched graft. * Determine cytomegalovirus-specific T-cells in product and donor graft. * Determine the genotype and phenotype of donor killer cell immunoglobulin-like receptor expression according to time after hematopoietic stem cell transplantation (HSCT). * Determine the reconstitution of NK function according to time after HSCT. * Determine the expression of NKG2 ligands of leukemic blasts. OUTLINE: Patients are stratified according to age (≤ 7 years vs \> 7 years). * Conditioning regimen: Patients 7 years of age or younger undergo total-body irradiation (TBI) twice daily on days -11 to -9. Patients over 7 years of age undergo TBI once on day -9. All patients receive thiotepa IV over 2 hours on days -8 and -7, fludarabine phosphate IV on days -6 to -3 and muromonab-CD3 on days -6 to 6. Patients with acute lymphoblastic leukemia or leukemia in the spinal fluid also receive methotrexate intrathecally prior to and after donor peripheral blood stem cell (PBSC) transplantation . * Donor PBSC transplantation: Patients undergo donor PBSC transplantation comprising CD34+ purified PBSCs and natural killer (NK) cells on day 0. Blood samples are collected in weeks 1-4, 6, 8, and 12. Analysis of samples includes quantitation of NK, NK-T, and T-cell subsets (CD3, CD4, and CD8) by flow cytometry; donor killer cell immunoglobulin-like receptor genotype and phenotype; interferon-gamma levels; and NK cytotoxicity. Samples are also analyzed by leukemic blast assay to determine if ligands that activate NK cells are expressed. After completion of study therapy, patients are followed periodically. PROJECTED ACCRUAL: A total of 20 patients will be accrued for this study.