Although haploidentical transplantation has proven curative for some patients, this procedure has been hindered by significant complications, primarily regimen-related toxicity including infection and graft versus host disease (GVHD). Building on prior institutional trials, this study will provide patients a haploidentical graft depleted of T lymphocytes using the investigational device, CliniMACS selection system. One week after the transplant procedure, patients will also receive an infusion of additional donor derived white blood cells called Natural Killer (NK) cells in an effort to decrease risks for rejection of the graft, disease relapse, and regimen related toxicity. The primary objective of the study is to evaluate 1 year survival in infants with high risk hematologic malignancies who receive this study treatment.