Neuroblastoma is a malignant tumor of the sympathetic nervous system. It is the second most common malignant tumor of childhood. Although modest advances have been made over the past 20 years children with high-risk neuroblastoma continue to have an unsatisfactory long-term survival. This study will administer induction chemotherapy followed by high-dose (myeloablative) chemotherapy with autologous stem cell transplantation, followed by radiation therapy, then immunotherapy with a non myeloablative allogeneic stem cell transplant for treatment of neuroblastoma. The purpose of this clinical research trial is to study the feasibility of giving immunotherapy with a non-myeloablative allogeneic transplant (NAT/AlloSCT), following myeloablative therapy and autologous stem cell transplant (MAT/AutoSCT). This study will also determine the side effects as well as the response rate for each group of patients (treatment arm).