Docetaxel, Trabectedin, and G-CSF or Pegfilgrastim in Treating Patients With Recurrent or Persistent Ovarian Epithelial Cancer, Primary Peritoneal Cavity Cancer, or Fallopian Tube Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal cavity carcinoma * Recurrent or persistent disease * Measurable disease, defined as at least 1 lesion that can be accurately measured in at least 1 dimension (longest dimension to be recorded) ≥ 20 mm by conventional techniques or ≥ 10 mm by spiral CT scan * Must have at least 1 "target lesion" to be used to assess response on this protocol as defined by RECIST criteria * Tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy * Must have had 1 prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organoplatinum compound and the initial treatment may have included high-dose therapy, consolidation, or extended therapy administered after surgical or non-surgical assessment * Patients are allowed, but not required to receive, 2 additional cytotoxic regimens for management of recurrent or persistent disease with no more than 1 non-platinum, non-taxane regimen * Patients who have received only 1 prior cytotoxic regimen (platinum-based regimen for management of primary disease), must meet 1 of the following criteria: * Platinum-free interval of \< 12 months * Progressed during platinum-based therapy * Persistent disease after a platinum-based therapy * Not eligible for a higher priority GOG protocol (i.e., any active GOG Phase III protocol for the same patient population) PATIENT CHARACTERISTICS: * GOG performance status (PS) 0-2 or after receiving 1 prior treatment regimen (GOG PS 0-1 after receiving 2 or more prior regimens) * Platelet count ≥ 100,000/mm³ * ANC count ≥ 1,500/mm³ * Hemoglobin \> 9 g/dL * Creatinine ≤ 1.5 times upper limit normal (ULN) * AST and ALT ≤ 2.5 times ULN * CPK normal * Bilirubin or direct bilirubin normal * Alkaline phosphatase normal * Neuropathy (sensory and motor) ≤ grade 1 * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No active infection requiring antibiotics (except for uncomplicated UTI) * No other invasive malignancy within the past 5 years, except nonmelanoma skin cancer * No known active liver disease or hepatitis * Willing and able to have a central venous catheter PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Recovered from effects of recent surgery, radiotherapy, or chemotherapy * At least 1 week since prior hormonal therapy directed at the malignant tumor * Continuation of hormone replacement therapy allowed * At least 3 weeks since other prior therapy, including biological and immunological therapy directed at the tumor * Chimeric or human or humanized monoclonal antibodies must be discontinued for at least 6 weeks prior to study entry * No investigational therapy within the past 30 days * No prior therapy with docetaxel and/or trabectedin * No radiation to more than 25% of marrow-bearing areas * No prior cancer treatment that contraindicates protocol therapy