Dasatinib in Treating Young Patients With Recurrent or Refractory Solid Tumors or Philadelphia Chromosome-Positive Acute Lymphoblastic Leukemia or Chronic Myelogenous Leukemia That Did Not Respond to Imatinib Mesylate

Inclusion Criteria: * Histologically confirmed diagnosis of 1 of the following: * Malignant extracranial solid tumor * Recurrent or refractory disease * Known bone marrow metastases\* allowed * Imatinib mesylate-resistant Philadelphia chromosome-positive (Ph+) acute lymphoblastic leukemia (ALL), defined as M3 bone marrow in a patient who previously received imatinib mesylate-containing treatment regimen * Imatinib mesylate-resistant Ph+ chronic myelogenous leukemia (CML), as defined by any of the following: * Increasing WBC or platelet count while on imatinib mesylate therapy * Lack of any cytogenetic response after an adequate duration of imatinib mesylate therapy, as defined by 1 of the following: * Failed to achieve a complete hematologic response after completion of 3 months of imatinib mesylate treatment * Failed to achieve a partial or complete cytogenetic response (i.e., ≤ 35% Ph+ cells) after 6 months of imatinib mesylate treatment * Appearance of accelerated or blastic feature while on imatinib mesylate therapy * Reappearance of Ph+ clones after an initial complete cytogenetic response to imatinib mesylate * More than 30% increase in Ph+ cells in peripheral blood or bone marrow cytogenetics while on imatinib mesylate therapy * Imatinib mesylate intolerance, as defined by development of adverse effects requiring discontinuation of imatinib mesylate therapy * Measurable disease (for patients with CML or ALL) * Determined by hematologic, cytogenetic, and molecular studies for CML * Determined by bone marrow blast percentage for ALL * Measurable or evaluable disease (for patients with solid tumors) * No known curative therapy or survival-prolonging therapy with an acceptable quality of life * No CNS solid tumors * CNS-positive leukemia allowed * Karnofsky performance status (PS) ≥ 50% (for patients \> 10 years of age) * Lansky PS ≥ 50% (for patients ≤ 10 years of age) * No evidence of graft-vs-host disease * Solid tumors: * Absolute neutrophil count ≥ 1,000/mm\^3 (750/mm\^3 if bone marrow infiltration) * Platelet count ≥ 100,000/mm\^3 (transfusion independent) (50,000/mm\^3 if bone marrow infiltration) * Hemoglobin ≥ 8.0 g/dL (red blood cell \[RBC\] transfusions allowed) * ALL/CML: * Platelet count ≥ 20,000/mm\^3 (platelet transfusions allowed) * Hemoglobin ≥ 8.0 g/dL (RBC transfusions allowed) * Creatinine clearance or radioisotope glomerular filtration rate ≥ 70 mL/min OR creatinine based on age, as follows: * No greater than 0.6 mg/dL (1-23 months of age) * No greater than 0.8 mg/dL (2- 5 years of age) * No greater than 1.0 mg/dL (6-9 years of age) * No greater than 1.2 mg/dL (10-12 years of age) * No greater than 1.4 mg/dL (13 years of age and over \[female\]) * No greater than 1.5 mg/dL (13-15 years of age \[male\]) * No greater than 1.7 mg/dL (16 years of age and over \[male\]) * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * ALT ≤ 110 U/L * Albumin ≥ 2 g/dL * Normal 12-lead EKG with corrected QTc \< 450 msec AND meets 1 of the following criteria: * Shortening fraction normal * Ejection fraction normal * No evidence of dyspnea at rest * No exercise intolerance * Pulse oximetry \> 94% if there is a clinical indication for determination * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No uncontrolled infection * No swallowing dysfunction that would prevent taking an oral or liquid medication * See Disease Characteristics * Recovered from prior chemotherapy, immunotherapy, or radiotherapy * No myelosuppressive chemotherapy within the past 3 weeks (6 weeks for nitrosoureas) * At least 7 days since prior growth factors * At least 14 days since prior pegfilgrastim * At least 7 days since prior biologic agents * At least 2 weeks since prior local small-port palliative radiotherapy * At least 3 months since prior total-body irradiation, craniospinal radiation, or radiation to ≥ 50% of the pelvis * At least 6 weeks since other prior substantial bone marrow radiation * At least 3 months since prior stem cell transplantation * Hydroxyurea cytoreduction for Ph+ leukemia allowed provided it is discontinued 24 hours before first dose of dasatinib * Prior intrathecal (IT) therapy allowed (for patients with CNS-positive leukemia) * Concurrent IT therapy comprising hydrocortisone, cytarabine, methotrexate, or cytarabine (liposomal) allowed (for patients with CNS-positive leukemia) * No other concurrent investigational drugs * No other concurrent anticancer agents, including chemotherapy, radiotherapy, immunotherapy, or biologic therapy * No concurrent enzyme-inducing anticonvulsants, including any of the following: * Phenytoin * Phenobarbital * Carbamazepine * Felbamate * Primdone * Oxcarbazepine * No concurrent antithrombotic or antiplatelet agents, including any of the following: * Warfarin * Heparin * Low-molecular weight heparin * Aspirin * Ibuprofen * Other nonsteroidal anti-inflammatory drugs * No concurrent CYP3A4 inhibitors, including itraconazole, ketoconazole, and voriconazole * No concurrent highly active antiretroviral treatment for HIV-positive patients