Lestaurtinib, Cytarabine, and Idarubicin in Treating Younger Patients With Relapsed or Refractory Acute Myeloid Leukemia

DISEASE CHARACTERISTICS: * Diagnosis of acute myeloid leukemia (AML) according to FAB classification * At least 5% blasts in the bone marrow, with or without extramedullary disease * In first relapse after induction therapy OR refractory to induction therapy with ≤ 1 attempt at remission induction * Patients who are in a first relapse \> 1 year from their initial diagnosis of AML are excluded from the dose-finding phase of the study, but are eligible for the efficacy phase * First relapse after hematopoietic stem cell transplantation (HSCT) allowed provided patient has no evidence of active graft-versus-host disease (GVHD) and is at least 4 months posttransplantation * Positive for a FLT3 activating mutation (internal tandem duplication or kinase domain point mutation) using standard polymerase chain reaction-based procedures at any time in the course of illness * Treatment-related AML allowed PATIENT CHARACTERISTICS: * Karnofsky performance status (PS) 50-100% (\> 16 years of age) OR Lansky PS 50-100% (≤ 16 years of age) * Creatinine clearance or radioisotope glomerular filtration rate ≥ 70 mL/min OR serum creatinine based on age and gender as follows: * Creatinine no greater than 0.4 mg/dL (1 month to \< 6 months of age) * Creatinine no greater than 0.5 mg/dL (6 months to \< 1 year of age) * Creatinine no greater than 0.6 mg/dL (1 year to \< 2 years of age) * Creatinine no greater than 0.8 mg/dL (2 years to \< 6 years of age) * Creatinine no greater than 1 mg/dL (6 years to \< 10 years of age) * Creatinine no greater than 1.2 mg/dL (10 years to \< 13 years of age) * Creatinine no greater than 1.4 mg/dL (females) or 1.5 mg/dL (males) (13 years to \< 16 years of age) * Creatinine no greater than 1.4 mg/dL (females) or 1.7 mg/dL (males) (16 years of age and over) * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * ALT \< 5 times ULN (unless it is related to leukemic involvement) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Shortening fraction ≥ 27% by echocardiogram OR ejection fraction ≥ 50% by radionuclide angiogram PRIOR CONCURRENT THERAPY: * Recovered from all prior therapy * No prior cumulative anthracycline doses exceeding 450 mg/m\^2 daunorubicin equivalents * Patients who relapse after receiving treatment on protocol COG-AAML03P1 or COG-AAML0531 (300 mg/m\^2 of daunorubicin hydrochloride and 48 mg/m\^2 of mitoxantrone hydrochloride) allowed provided they have not received any additional anthracyclines * At least 14 days since prior cytotoxic therapy * Hydroxyurea allowed to decrease the WBC prior to starting protocol treatment * No concurrent hydroxyurea * At least 7 days since prior biologic agents * At least 14 days since prior monoclonal antibody therapy * Radiotherapy to chloromas allowed * Irradiated lesion may not be used to assess tumor response * No other concurrent chemotherapy, investigational therapy, immunomodulating agents, or steroids * Steroids used as an antiemetic allowed * Prophylactic intrathecal cytarabine allowed * No concurrent CYP3A4,5 inhibitors, including any of the following: * Azole antifungals (e.g., fluconazole or voriconazole) * Cyclosporine * Erythromycin * Clarithromycin * Troleandomycin * HIV protease inhibitors * Nefazodone * No concurrent CYP3A4,5 inducers, including any of the following: * Carbamazepine * Dexamethasone * Rifampin * Phenobarbital * Phenytoin * Hypericum perforatum (St. John's wort)