Trabectedin in Treating Young Patients With Recurrent or Refractory Soft Tissue Sarcoma or Ewing's Family of Tumors

Inclusion Criteria: * Patients must be greater than or equal to 12 months of age at the time of study entry and no more than 21 years of age when initially diagnosed with the malignancy to be treated on this protocol * Histologically confirmed recurrent or refractory sarcoma tumors, including the following: * Rhabdomyosarcoma * Nonrhabdomyosarcomatous soft tissue sarcoma * Ewing's sarcoma * Measurable disease by imaging studies * Lesions assessable only by radionuclide scans are not considered measurable * If the only measurable lesion has been previously irradiated, then that lesion must have shown evidence of an interim increase in size * No significant amount of metastatic liver disease, defined as the following: * Lesions occupying more than 25% of the liver by imaging and abnormal liver function tests or abnormal synthetic liver function * Performance status - Lansky 50-100% (10 years of age and under) * Performance status - Karnofsky 50-100% (over 10 years of age) * Absolute neutrophil count at least 1,000/mm\^3 * Platelet count at least 100,000/mm\^3 (transfusion independent) * Hemoglobin at least 8.0 g/dL (transfusion allowed) * No concurrent CYP3A4 inhibitors, including the following: * Grapefruit juice * Erythromycin * Azithromycin * Clarithromycin * Rifampin and its analogs * Fluconazole * Ketoconazole * Itraconazole * Cimetidine * Cannabinoids (marijuana or dronabinol) * Leukotriene inhibitors used in asthma (e.g., zafirlukas…