S0904: Docetaxel With or Without Vandetanib in Treating Patients With Persistent or Recurrent Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Primary Peritoneal Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal carcinoma * Recurrent, refractory, or progressive/persistent disease * Measurable or non-measurable disease documented by CT scan of the abdomen and pelvis * Must have received 1 prior platinum-based chemotherapy regimen for management of primary disease containing carboplatin, cisplatin, or other organoplatinum compound * Initial treatment may have included any of the following: * High-dose therapy * Consolidation therapy * Non-cytotoxic agent therapy * Extended therapy administered after surgical or non-surgical assessment * Additional cytotoxic regimen for recurrent, refractory, or progressive/persistent disease, including re-treatment with primary treatment regimen * No more than 3 prior regimens for recurrent, refractory, persistent, or progressive disease. PATIENT CHARACTERISTICS: * Zubrod performance status 0-2 * Absolute neutrophil count (ANC) ≥ 1,500/mcl * Platelet count ≥ 100,000/mcl * Serum creatinine normal OR calculated creatinine clearance ≥ 30 mL/min * Urine protein:creatinine ratio \< 1 * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * aspartate aminotransferase - alanine aminotransferase (AST or ALT) ≤ 2.5 times ULN (≤ 5 times ULN if liver metastases are present) * Alkaline phosphatase ≤ 2.5 times ULN (≤ 5 times ULN if liver metastases are present) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 6 months after completion of vandetanib therapy * No neuropathy ≥ grade 2 CTCAE v4.0 * No active infection requiring systemic or intravenous antibiotics * No significant traumatic injury within the past 28 days * No significant cardiovascular disease, including any of the following: * Uncontrolled hypertension (i.e., systolic blood pressure \[BP\] \> 140 mm Hg or diastolic BP \> 90 mm Hg) within the past 28 days * Myocardial infarction superior vena cava syndrome, or New York Heart Association (NYHA) class II-IV heart disease within the past 3 months * Presence of left bundle branch block * Congenital long QT syndrome or first degree relative with unexplained sudden death \< 40 years of age * QT interval with Bazett's correction that is unmeasurable or ≥ 480 msec by screening ECG * History of symptomatic arrhythmia (i.e., multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia, or uncontrolled atrial fibrillation) requiring treatment (≥ CTCAE grade 3) or asymptomatic sustained ventricular tachycardia * Atrial fibrillation controlled on medication allowed PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Recovered from all prior therapy (except alopecia) to NCI CTCAE v3.0 grade ≤ 1 * No prior vandetanib * Treatment with other anti-vascular endothelial growth factor (VEGF) targeted therapy allowed * No prior docetaxel or any non-cytotoxic therapy (excluding hormonal therapy) for recurrent disease, regardless of whether it was part of primary treatment * Prior docetaxel as part of front-line cytotoxic regimen (including maintenance therapy) allowed as long as no disease progression on or within 6 months after receiving docetaxel * At least 7 days since prior hormonal therapy for the malignant tumor * Concurrent hormone replacement therapy for menopausal symptoms allowed * At least 28 days since other prior therapy for the malignant tumor, including immunologic agents * More than 7 days since prior minor surgical procedures, fine needle aspirates, or core biopsies * More than 14 days since prior and no concurrent potent inducers of cytochrome P450 3A4 (CYP3A4) function * More than 14 days since prior and no concurrent medications having a risk of causing Torsades de Pointes or risk of QTc prolongation * Patients receiving a drug that has a risk of QTc prolongation must not have QTc ≥ 460 msec * More than 28 days since prior investigational agents for any purpose * More than 28 days since prior and no concurrent major surgical procedure or open biopsy * More than 5 years since prior chemotherapy for abdominal or pelvic tumor, except treatment of ovarian, fallopian tube, or primary peritoneal cancer * Prior adjuvant chemotherapy for localized breast cancer allowed, provided it was completed more than 3 years prior to study, and the patient remains free of recurrent or metastatic disease * More than 5 years since prior radiotherapy to any portion of the abdominal cavity or pelvis, except for the treatment of ovarian, fallopian tube, or primary peritoneal cancer * Prior radiotherapy for localized cancer of the breast, head and neck, or skin allowed, provided it was completed more than 3 years prior to study, and the patient remains free of recurrent or metastatic disease * No prior radiation to more than 25% of marrow-bearing areas * More than 28 days since prior radiotherapy * No other concurrent investigational or commercial agents