Pazopanib Hydrochloride in Treating Young Patients With Solid Tumors That Have Relapsed or Not Responded to Treatment

Inclusion Criteria: * Diagnosis of 1 of the following: NOTE: Histologic confirmation not required for intrinsic brain stem cell tumor, optic pathway gliomas, pineal tumors and elevations of cerebrospinal fluid, and serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin. * Histologically confirmed relapsed or refractory solid tumors at original diagnosis including CNS tumors\* (Part 1 and Part 2a) * Neurologic deficits in patients with CNS tumors must have been relatively stable for ≥ 1 week * Histologically confirmed soft tissue sarcoma, desmoplastic small round cell tumor, or extraosseus Ewing sarcoma at original diagnosis including the following (Part 2b): * Tumor in the head, neck, or extremity or fixed within the abdomen or pelvis that it is not sensitive to motion artifact * No isolated pulmonary metastases * Disease with no known curative therapy or no therapy proven to prolong survival with acceptable quality of life * Measurable or evaluable disease (Part 1 and Part 2a) * Measurable tumor that is ≥ 2 cm in its longest diameter (Part 2b) * Patients must be: * \> 2 years of age and ≤ 21 years of age (Part 1 and Part 2a) * \> 2 years of age and ≤ 25 years of age (Part 2b) * Body surface area ≥ 0.48 m\^2 (Part 1 and Part 2b) * For patients with CNS tumors or CNS metastasis, there must be no evidence of new CNS hemorrhage of more than punctate size and/or \> 3 foci of punctate hemorrhage on baseline MRI for primary CNS tumors ≥ 14 days prior to study entry * Karnofsky performance status (PS) 50-100% (\> 16 years of age) * Lansky PS 50-100% (≤ 16 years of age) * Platelet count ≥ 100,000/mm\^3 (transfusion independent) * ANC ≥ 1,000/mm\^3 * Hemoglobin ≥ 8.0 g/dL (may receive RBC transfusions) * Creatinine clearance or radioisotope GFR ≥ 70 mL/min OR serum creatinine based on age/gender as follows: * 0.6 mg/dL (1 to \< 2 years of age) * 0.8 mg/dL (2 to \< 6 years of age) * 1 mg/dL (6 to \< 10 years of age) * 1.2 mg/dL (10 to \< 13 years of age) * 1.5 mg/dL (male ) or 1.4 mg/dL (female) (13 to \< 16 years of age) * 1.7 mg/dL (male) or 1.4 mg/dL (female) ( ≥ 16 years of age) * Urine protein:creatinine ratio \< 1 OR urinalysis negative for protein OR 24-hour urine protein level \< 1 g * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * ALT ≤ 110 U/L * PT and PTT ≤ 1.2 times ULN * INR ≤ 1.2 * Serum albumin ≥ 2 g/dL * No grade \> 1 abnormalities of potassium, calcium, magnesium, or phosphorous * Supplementation allowed * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Oral contraceptives are not considered effective * Adequate cardiac function defined as any of the following: * Shortening fraction of ≥ 27% by echocardiogram * Ejection fraction of ≥ 50% by gated radionuclide study * QTc \< 450 msec * No history of myocardial infarction, severe or unstable angina, or peripheral vascular disease or familial QTc prolongation * Adequate blood pressure defined as ≤ 95th percentile for age, height, and gender * Known history of well-controlled seizures allowed * Able to swallow whole tablets (Part 1 and Part 2b) * No uncontrolled infection * No evidence of active bleeding, intratumoral hemorrhage, or bleeding diathesis * None of the following conditions within the past 6 months: * Arterial thromboembolic events, including transient ischemic attack or cerebrovascular accident * Pulmonary embolism * Deep vein thrombosis * Other venous thromboembolic event * No hemoptysis within the past 6 weeks * No serious or non-healing wound, ulcer, or bone fracture * No significant traumatic injury within the past 28 days * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 28 days * No patients who, in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study * No fine-needle aspiration within 48 hours before day 1 of therapy * Fully recovered from all prior therapy (e.g., chemotherapy, immunotherapy, or radiotherapy) * At least 3 weeks since prior myelosuppressive chemotherapy (6 weeks for prior nitrosourea) * At least 7 days since prior hematopoietic growth factor * At least 21 days since prior VEGF-Trap * No prior pazopanib hydrochloride * At least 7 days since prior VEGF-blocking tyrosine kinase inhibitor or other biological agents * At least 3 half-lives since prior monoclonal antibody, including bevacizumab * At least 21 days since any other prior anticancer antibody therapy * At least 2 weeks since prior local palliative radiotherapy (small port) * At least 3 months since prior total-body irradiation, craniospinal radiotherapy, or ≥ 50% radiotherapy to the pelvis * At least 6 weeks since prior other substantial bone marrow radiotherapy * At least 2 months since stem cell transplantation and no evidence of graft-vs-host disease * Thyroid replacement therapy allowed provided a stable dose has been received for ≥ 4 weeks * No concurrent medication for cardiac function or hypertension * Concurrent corticosteroids allowed provided dose is stable or decreasing for \> 7 days (for patients enrolled in Part 1 and Part 2a of study) * No concurrent corticosteroids for patients enrolled in Part 2b of the study * No other concurrent anticancer agents or radiotherapy * No other concurrent investigational drugs * No concurrent enzyme-inducing anticonvulsants * No concurrent anticoagulation therapy with coumadin and/or low molecular weight heparin * Prophylactic anticoagulation therapy (i.e., intraluminal heparin) of venous or arterial access devices allowed * No concurrent aspirin, ibuprofen, or other NSAIDs * No concurrent drugs metabolized through several of the specific P450 cytochrome isoform including inducers or inhibitors of CYP3A4 * No concurrent drugs with a known risk of torsades de pointes * At least 28 days since prior major surgical procedure, laparoscopic procedure, or open biopsy * Port placement or central line placement 48 hours before day 1 of therapy allowed * No core biopsy within the past 7 days