This is a pilot clinical trial investigating the addition of haploidentical natural killer cell infusion to autologous stem cell transplantation. This intervention will be evaluated in children with high-risk solid tumors for whom autologous transplantation is indicated. Natural killer cells from a haploidentical family member will be given after high dose chemotherapy and positively selected autologous stem cells. In patients with neuroblastoma, the anti-GD2 antibody hu14.18K322A will also be given. The effect on normal hematopoietic cell recovery will be evaluated and survival of children treated with this approach will be determined.