Irinotecan Hydrochloride and Temozolomide With Temsirolimus or Dinutuximab in Treating Younger Patients With Refractory or Relapsed Neuroblastoma

Inclusion Criteria: * Patients must have had histologic verification of neuroblastoma or ganglioneuroblastoma or demonstration of neuroblastoma cells in the bone marrow with elevated urinary catecholamines (i.e., \> 2 x upper limit of normal \[ULN\]), at the time of initial diagnosis * For the purposes of this study, aggressive multidrug chemotherapy is defined as chemotherapy including 2 or more agents that must include an alkylating agent and a platinum-containing compound; patients must have ONE of the following: * First episode of recurrent disease following completion of aggressive multi-drug frontline therapy * First episode of progressive disease during aggressive multi-drug frontline therapy * Primary resistant/refractory disease (less than partial response by INRC) detected at the conclusion of at least 4 cycles of aggressive multidrug induction chemotherapy on or according to a high-risk neuroblastoma protocol (examples include A3973, ANBL0532, ANBL09P1, etc.) * Patients must have at least ONE of the following: * Measurable tumor on magnetic resonance imaging (MRI), computed tomography (CT) scan obtained within 3 weeks prior to study entry; measurable is defined as \>= 10 mm in at least one dimension on spiral/helical CT that is metaiodobenzylguanidine (MIBG) avid or demonstrates increased fludeoxyglucose (FDG) uptake on positron emission tomography (PET) scan * MIBG scan obtained within 3 weeks prior to study entry with positive uptake at a minimum of one site; this site must represent disease recurrence after completion of therapy, progressive disease on therapy, or refractory disease during induction * Patients with resistant/refractory soft tissue disease that is not MIBG avid or does not demonstrate increased FDG uptake on PET scan must undergo biopsy to document the presence of viable neuroblastoma; biopsy is not required for patients who have new site of soft tissue disease (radiographic evidence of disease progression) regardless of whether progression occurs while receiving therapy or after completion of therapy * Note: Patients with elevated catecholamines (i.e., \> 2 x ULN) only or bone marrow disease only are NOT eligible for this study * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age * Patients must have received frontline therapy (including surgery, chemotherapy, autologous stem cell transplant \[SCT\] +/- MIBG, immunotherapy, radiotherapy, and retinoids) but may NOT have received second line chemotherapy for resistant/refractory, relapsed disease or progressive disease * At least 14 days must have elapsed since completion of myelosuppressive therapy * At least 7 days must have elapsed since the completion of therapy with a non-myelosuppressive biologic agent or retinoid * No interim time prior to study entry is required following prior radiation therapy (RT) for non-target lesions; however, patients must not have received radiation for a minimum of 4 weeks prior to study entry at the site of any lesion that will be identified as a target lesion to measure tumor response; lesions that have been previously radiated cannot be used as target lesions unless there is radiographic evidence of progression at the site following radiation or a biopsy done following radiation shows viable neuroblastoma; palliative radiation is allowed to sites that will not be used to measure response during this study * Patients are eligible \>= 6 weeks after autologous stem cell transplants or stem cell infusions as long as hematologic and other eligibility criteria have been met * Patients are eligible \>= 6 weeks after therapeutic 131I-MIBG provided that all other eligibility criteria are met * Subjects who have previously received anti-GD2 monoclonal antibodies for biologic therapy or for tumor imaging are eligible unless they have had progressive disease while receiving prior anti-GD2 therapy; subjects who have received autologous marrow infusions or autologous stem cell infusions that were purged using monoclonal antibody linked to beads, but no other form of anti-GD2 monoclonal antibody, are eligible * Patients must not have received long-acting myeloid growth factors (e.g., Neulasta) within 14 days of entry on this study; seven days must have elapsed since administration of a short acting myeloid growth factor * Peripheral absolute neutrophil count (ANC) \>= 750/uL * Platelet count \>= 75,000/uL (transfusion independent) * Patients known to have bone marrow involvement with neuroblastoma are eligible provided that minimum ANC and platelet count criteria are met but are not evaluable for hematological toxicity * Creatinine clearance or estimated radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or * A serum creatinine =\< upper limit of normal (ULN) based on age/gender as follows: * Age 1 month to \< 6 months: 0.4 for males, 0.4 for females * Age 6 months to \< 1 year: 0.5 for males, 0.5 for females * Age 1 to \< 2 years: 0.6 for males, 0.6 for females * Age 2 to \< 6 years: 0.8 for males, 0.8 for females * Age 6 to \< 10 years: 1 for males, 1 for females * Age 10 to \< 13 years: 1.2 for males, 1.2 for females * Age 13 to \< 16 years: 1.5 for males, 1.4 for females * Age \>= 16 years: 1.7 for males, 1.4 for females * Total bilirubin =\< 1.5 x ULN for age AND * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 5.0 x ULN for age (=\< 225 U/L); for the purpose of this study, the ULN for SGPT is 45 U/L * Adequate central nervous system function defined as: * Patients with a history of central nervous system (CNS) disease must have no clinical or radiological evidence of CNS disease at the time of study enrollment * Patients with seizure disorders may be enrolled if seizures are well controlled on anticonvulsants * CNS toxicity =\< grade 2 * Shortening fraction of \>= 27% by echocardiogram (ECHO) OR * Ejection fraction \>= 50% by ECHO or gated radionuclide study * Adequate coagulation defined as: * Prothrombin time (PT) =\< 1.2 x upper limit of normal * Adequate pulmonary function defined as: * No evidence of dyspnea at rest, no exercise intolerance, no chronic oxygen requirement, and room air pulse oximetry \> 94% if there is a clinical indication for pulse oximetry; normal pulmonary function tests in patients who are capable of cooperating with testing (including diffusion capacity of the lung of carbon monoxide \[DLCO\]) are required if there is a clinical indication for determination; for patients who do not have respiratory symptoms, full pulmonary function tests (PFTs) are NOT required Exclusion Criteria: * Men and women of childbearing potential and their partners must agree to use adequate contraception while enrolled on this study; based on the established teratogenic potential of alkylating agents, pregnant women will be excluded from this study; female patients who are lactating must agree to stop breastfeeding or will otherwise be excluded from this study; females of childbearing potential must have a negative pregnancy test to be eligible for this study * Patients with elevated catecholamines (i.e., \> 2 x ULN) only or bone marrow disease only are NOT eligible for this study * Patients must have been off pharmacologic doses of systemic steroids for at least 7 days prior to enrollment; patients who require or are likely to require pharmacologic doses of systemic corticosteroids while receiving treatment on this study are ineligible; the only exception is for patients known to require 2 mg/kg or less of hydrocortisone (or an equivalent dose of an alternative corticosteroid) as premedication for blood product administration in order to avoid allergic transfusion reactions; the use of conventional doses of inhaled steroids for the treatment of asthma is permitted, as is the use of physiologic doses of steroids for patients with known adrenal insufficiency * Patients must not have received enzyme-inducing anticonvulsants including phenytoin, phenobarbital, valproic acid, or carbamazepine for at least 7 days prior to study enrollment; patients receiving non-enzyme inducing anticonvulsants such as gabapentin or levetiracetam will be eligible * Patients must not have been diagnosed with myelodysplastic syndrome or with any malignancy other than neuroblastoma * Patients with symptoms of congestive heart failure are not eligible * Patients must not have \>= grade 2 diarrhea * Patients must not have uncontrolled infection * Patients with a history of grade 4 allergic reactions to anti-GD2 antibodies or reactions that required discontinuation of the anti-GD2 therapy are not eligible * Patients with a significant intercurrent illness (any ongoing serious medical problem unrelated to cancer or its treatment) that is not covered by the detailed exclusion criteria and that is expected to interfere with the action of study agents or to significantly increase the severity of the toxicities experienced from study treatment are not eligible