Paclitaxel and Carboplatin or Ifosfamide in Treating Patients With Newly Diagnosed, Persistent or Recurrent Uterine, Ovarian, Fallopian Tube, or Peritoneal Cavity Cancer

PRIMARY OBJECTIVES: I. To determine if treatment with combination paclitaxel and carboplatin (TC) chemotherapy does not result in an inferior death rate when compared to ifosfamide, mesna, and paclitaxel chemotherapy. SECONDARY OBJECTIVES: I. To determine if treatment with combination paclitaxel and carboplatin (TC) chemotherapy does not result in an inferior progression-free survival when compared to ifosfamide, mesna, and paclitaxel chemotherapy. II. To determine if acute toxicity, specifically physician-assessed neurotoxicity and infection, associated with combination paclitaxel and carboplatin chemotherapy is reduced compared to that of ifosfamide, mesna, and paclitaxel chemotherapy. III. To determine if treatment with combination paclitaxel and carboplatin chemotherapy is associated with superior patient-reported quality of life and neurotoxicity scores compared to that of ifosfamide, mesna, and paclitaxel chemotherapy. TERTIARY OBJECTIVES: I. To bank formalin-fixed, paraffin-embedded (FFPE) tumor tissue and deoxyribonucleic acid (DNA) extracted from whole blood for future research. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients receive paclitaxel intravenously (IV) over 3 hours followed by carboplatin IV over 30-60 minutes on day 1. ARM II: Patients receive ifosfamide IV over 1 hour on days 1-3 followed by paclitaxel as in Arm I. In both arms, treatment repeats every 21 days for 6-10 courses in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for 2 years, every 6 months for 3 years, and then annually thereafter.