Combination Chemotherapy, Monoclonal Antibody, and Natural Killer Cells in Treating Young Patients With Recurrent or Refractory Neuroblastoma

INCLUSION CRITERIA (Participant): * Diagnosis of recurrent or refractory neuroblastoma. * Age \< 22 years at the time of enrollment. * Measurable or evaluable (detectable by bone scan or MIBG, but not measurable) disease. * Organ function: Must have adequate organ and marrow function as defined by the following parameters: * Bone marrow: Absolute neutrophil count (ANC) \> 750/mm3; Platelets \> 75,000/mm3 (no platelet transfusions for at least 1 week) * Hepatic: Total bilirubin ≤ 2 x upper limit of normal (ULN) for age; SGPT (ALT) ≤ 2.5 x ULN for age. * Renal: Creatinine clearance or radioisotope GFR equal to or \>70 ml/min/1.73m2 OR serum creatinine based on age as follows: * Age 5 years of age and under, then maximum serum creatinine 0.8 mg/dL * Age \>5 and equal to or \<10 years, then maximum serum creatinine 1.0 mg/dL * Age \>10 and equal to or \<15 years, then maximum serum creatinine 1.2 mg/dL * Age \>15 years, then maximum serum creatinine 1.5 mg/dL * Cardiovascular: Shortening fraction \> or equal to 27% by echocardiogram; Corrected QT interval \< or equal to 450 milliseconds * Performance status: Karnofsky \> or equal to 50 for \> 10 years of age; Lansky \> or equal to 50 for children equal to or \< 10 years of age. * Prior therapy: Participant must have fully recovered from the acute toxic effects of all prior therapy prior to enrolling on study. * Myelosuppressive chemotherapy: Must not have received myelosuppressive therapy within 2 weeks prior to study entry (4 weeks if nitrosurea). * Biologic (anti-neoplastic agent): At least 7 days since the completion of therapy with biologic agent, including retinoic acid. At least 6 weeks must have elapsed since prior therapy that includes a monoclonal antibody. Participants receiving IVIG are eligible; however, participant must not receive IVIG during the 4 days of antibody infusion. * Radiation therapy: At least 2 weeks since prior local radiation therapy at the time of study entry. * Growth factors: Must not have received hematopoietic growth factors (G-CSF, GM-CSF) for at least 1 week prior to study entry. * Investigational agent: Must not have received investigational agent within 7 days of study entry. * Immune therapy: Must not have received immunosuppressive (including glucocorticoids), immunostimulatory or any immunomodulatory treatment within 2 weeks of study entry. Steroid containing inhalers, steroid replacement for adrenal insufficiency and steroid premedication for prevention of transfusion or imaging contrast-agent related allergic reaction will be permitted. * Participants may have had prior CNS metastasis providing: CNS disease has been previously treated and CNS disease has been clinically stable for 4 weeks prior to study entry (assessment must be made by CT or MRI). * Written informed consent following institutional and federal guidelines. EXCLUSION CRITERIA (Participant): * Prior monoclonal antibody: Participants having received in vivo monoclonal anti-GD2 antibodies for biologic therapy or for tumor imaging are ineligible if they have experienced a severe allergic reaction while receiving prior anti-GD2 therapy. * Pregnancy or breast feeding: Study participants who are pregnant are not eligible for this study. Pregnancy tests must be obtained in girls who are \> 10 years of age or post-menarchal within 7 days prior to study enrollment. Males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method during participation in the trial. Breast feeding should be discontinued if a mother wishes to participate in this study. * Allergy: Known hypersensitivity to other recombinant human antibodies. * An uncontrolled infection. * Participants who have not started protocol therapy within 7 days of study enrollment. INCLUSION CRITERIA (Donor): * Donor is a partially matched family member. * Donor is HIV negative. * Donor is at least 18 years of age. * Donor is not pregnant. * Donor does not have any other medical condition that, in the opinion of an independent physician, precludes performance of an apheresis procedure.