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

Inclusion Criteria:

* Patients must have newly diagnosed stage I-IV, persistent or recurrent (including unstaged) uterine carcinosarcoma (malignant mixed mullerian tumor-MMMT or with ovarian, fallopian tube or peritoneal carcinosarcoma and an enrollment date prior to 10/21/2013; pathology confirmed by site/institutional pathologist prior to enrollment) and be chemotherapy naïve as directed against their carcinosarcoma; unstaged patients (patients who have not had hysterectomy or ovarian surgery) are eligible and should be included as "unstaged" if the only histologic (pathology) documentation of the disease is a biopsy or curettage of the uterus; if these patients have documented metastatic disease, it should be assigned the appropriate stage (III/IV)
* Patients may have received prior adjuvant external beam radiation therapy and/or vaginal brachytherapy; patients should be at least 4 weeks from the completion of external beam radiotherapy prior to beginning protocol chemotherapy; patients do not need to be delayed if receiving vaginal brachytherapy only
* Gynecologic Oncology Group (GOG) performance status 0, 1, or 2
* Patients must have recovered from the effects of recent surgery, radiotherapy, or other therapy
* Patients must be free of active infection requiring antibiotics
* Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to beginning protocol chemotherapy; continuation of hormone replacement therapy is permitted
* Platelet count greater than or equal to 100,000/mcL
* Absolute neutrophil count (ANC) greater than or equal to 1,500/mcL equivalent to Common Terminology Criteria for Adverse Events (CTCAE) version (v)3.0 grade 1
* Creatinine less than or equal to 1.5 times upper limit of normal (ULN), CTCAE v3.0 grade 1
* Bilirubin less than or equal to 1.5 times ULN (CTCAE v3.0 grade 1)
* Serum glutamic oxaloacetic transaminase (SGOT) less than or equal to 2.5 times ULN (CTCAE v3.0 grade 1)
* Alkaline phosphatase less than or equal to 2.5 times ULN (CTCAE v3.0 grade 1)
* Serum albumin should be equal to or greater than 3 g/dL
* Neuropathy (sensory and motor) less than or equal to CTCAE v3.0 grade 1
* Patients must have signed an approved informed consent and authorization permitting release of personal health information
* Patients of childbearing potential must have a negative serum pregnancy test prior to study entry and be practicing an effective form of contraception
* Patients may have measurable disease or non-measurable disease; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be \>= 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or \>= 10 mm when measured by spiral CT; measurable disease patients must have at least one "target lesion" to be used to assess progression on this protocol as defined by Response Evaluation Criteria In Solid Tumors (RECIST); 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

Exclusion Criteria:

* Patients who have received prior cytotoxic chemotherapy for management of uterine or ovarian carcinosarcoma
* Patients with a history of other invasive malignancies or with a concomitant invasive malignancy, with the exception of non-melanoma skin cancer, if there is any evidence of other malignancy being present within the last five years; patients are also ineligible if their previous cancer treatment contraindicates this protocol therapy
* Patients for whom radiotherapy is planned after or during chemotherapy prior to progression of cancer
* Patients with known hypersensitivity to Escherichia (E.) coli-derived drug preparations (pegfilgrastim and filgrastim \[G-CSF\])
* Patients with a known hypersensitivity to mesna or other thiol compounds
* For enrollment prior to 10/21/2013, patients who are not biopsy proven to have carcinosarcoma of the uterus, fallopian tube, peritoneum or ovary; for enrollment after 10/21/2013, patients who are not biopsy proven to have carcinosarcoma of the uterus