Monoclonal Antibody Therapy With Sargramostim and Interleukin-2 in Treating Children With Neuroblastoma

Inclusion Criteria: * Must have recently completed a course of myeloablative therapy followed by autologous stem cell (bone marrow or peripheral blood) rescue (ASCT) * Patients must have a diagnosis of neuroblastoma based upon tumor histology or bone marrow metastases and elevated urine catecholamine metabolites; greater than 98% of neuroblastomas are GD2-positive without intratumor heterogeneity, so these tumors will not be immunostained prior to study entry * Patients entered on CCG-3951 may become eligible following the third course of high-dose chemotherapy followed by peripheral blood stem cell (PBSC) rescue; patients treated on institutional (local) protocols of high-dose chemotherapy with PBSC rescue may also become eligible after one or more courses of PBSC rescue * Patients must enter onto study within 8 weeks after the total absolute phagocyte count \[neutrophils (segs + bands) + monocytes\] is \> 1,000/uL; the APC criteria include counts obtained while on G-CSF therapy * Patients must have a performance status of 0, 1 or 2 and patients must have a life expectancy of \>= 2 months * Serum creatinine =\< 1.5 x normal, or creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 60 ml/min/1.73 m\^2 * Total bilirubin =\< 1.5 x normal * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) or serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 5 x normal * Veno-occlusive disease, if present, should be stable or improving * Shortening fraction of \>= 27% by echocardiogram, or ejection fraction of \> 50% by gated radionuclide study * Forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) \> 60% of predicted by pulmonary function test * For children who are unable to do pulmonary function tests (PFTs), no evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \> 94% on room air * Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled * Central nervous system (CNS) toxicity \< grade 2 * Patients must have a double lumen catheter or single lumen and peripheral IV so that interleukin (IL)-2 and ch14.18 can be given separately * Patients who remain evaluable for response on Phase II/III studies (i.e. CCG-3891) are not eligible for this study; however, patients treated on Phase I studies (i.e. CCG-3951) and patients who are no longer evaluable on Phase II/III studies (i.e. progressive disease following therapy) will be eligible * Patients who were previously treated with antibody 14.G2a or ch14.18 are ineligible for this study * Patients requiring chronic use of corticosteroids are ineligible * Corticosteroid, immunosuppressive drugs, myelosuppressive chemotherapy, and retinoic acid must not be given within 14 days prior to study entry * Radiation therapy must not be given within seven days prior to study entry or during therapy * All patients and/or their parents or legal guardians must sign a written informed consent * All institutional, FDA, and NCI requirements for human studies must be met