Inclusion Criteria:

* Patients with newly diagnosed embryonal RMS, botryoid or spindle cell variants of embryonal RMS, ectomesenchymoma, or alveolar RMS are eligible for this study
* Enrollment on COG-D9902 to confirm local histologic diagnosis with central pathology review is required for all patients
* Patients may be enrolled on ARST0531 and start protocol treatment prior to receipt of central pathology review results
* Patient must have Intermediate-risk RMS defined as:

* Embryonal, botryoid, or spindle cell RMS, or ectomesenchymoma: stage 2 or 3 and group III OR
* Alveolar RMS: stage 1-3 and group I-III
* Staging ipsilateral retroperitoneal lymph node dissection (SIRLND) is required for all patients >= 10 years of age with paratesticular tumors and for patients < 10 years with clinically or radiographically involved lymph nodes (except when extensive lymph node involvement, defined as two or more lymph nodes > 2 cm in dimension, is identified by imaging studies)
* Regional lymph node sampling or sentinel lymph node procedure is required for histologic evaluation in patients with extremity tumors
* Clinically or radiographically enlarged nodes should be sampled for histologic evaluation
* Detection of metastasis by optional FDG PET (not required for study enrollment); FDG PET may detect abnormalities suggestive of metastasis not identified by bone scan, computed tomography (CT), or bone marrow aspiration/biopsy; the prognostic significance of FDG PET-detected abnormalities is not clear; FDG PET-detected abnormalities MUST be confirmed to be metastases by an additional imaging modality (such as magnetic resonance imaging \[MRI\] or CT) OR pathologic confirmation; unless FDG PET abnormalities are confirmed by another imaging modality or biopsy, FDG PET abnormalities will NOT be considered evidence of metastasis
* Patients must have a performance status of 0, 1, or 2; the Lansky performance score should be used for patients < 16 years and the Karnofsky performance score for patients >= 16 years
* Patients who have received prior chemotherapy (excluding steroids) or radiation therapy, except for patients transferring from ARST0331 (low-risk study), are not eligible
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70 ml/min/1.73 m\^2 or a serum creatinine based on age/gender as follows:

* 1 month to < 6 months: 0.4 mg/dL
* 6 months to < 1 year: 0.5 mg/dL
* 1 to < 2 years: 0.6 mg/dL
* 2 to < 6 years: 0.8 mgt/dL
* 6 to < 10 years: 1 mg/dL
* 10 to < 13 years: 1.2 mg/dL
* 13 to < 16 years: 1.5 mg/dL (males) or 1.4 mg/dL (females)
* >= 16 years: 1.7 mg/dL (males) or 1.4 mg/dL (females)
* Patients with urinary tract obstruction by tumor must meet the renal function criteria AND must have unimpeded urinary flow established via decompression of the obstructed portion of the urinary tract
* Total bilirubin =< 1.5 x upper limit of normal for age
* Peripheral absolute neutrophil count (ANC) >= 750/uL
* Platelet count >= 75,000/uL (transfusion independent)
* No evidence of uncontrolled infection
* Patients must be able to undergo radiation therapy, if necessary, as specified in the protocol
* Female patients of childbearing potential must have a negative pregnancy test
* Female patients who are breast feeding must agree to stop breast feeding
* Sexually active patients of childbearing potential must be willing to use effective contraception during therapy and for at least 1 month after treatment is completed
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met