Combination Chemotherapy With or Without Temsirolimus in Treating Patients With Intermediate Risk Rhabdomyosarcoma

Inclusion Criteria: * Feasibility Phase: Patients must be \< 21 years of age at the time of enrollment; please note: the feasibility phase is complete, effective with amendment #1 * Efficacy Phase: Patients must be =\< 40 years of age at the time of enrollment * Patients with newly diagnosed RMS of any subtype, except adult-type pleomorphic, based upon institutional histopathologic classification, are eligible to enroll on the study based upon stage, group, and age, as below * RMS types included under embryonal rhabdomyosarcoma (ERMS) include those classified in the 1995 International Classification of Rhabdomyosarcoma (ICR) as ERMS (classic, spindle cell, and botryoid variants), which are reclassified in the 2013 World Health Organization (WHO) classification as ERMS (classic, dense and botryoid variants) and spindle cell/sclerosing RMS (encompassing the historical spindle cell ERMS variant and the newly recognized sclerosing RMS variant); classification of alveolar rhabdomyosarcoma (ARMS) in the 2013 WHO classification is the same as in the ICR and includes classic and solid variants * ERMS * Stage 1, group III (non-orbit) * Stage 3, group I/II * Stage 2/3, group III * Stage 4, group IV, \< 10 years old * ARMS: * Stages 1-3, groups I-III * Specimen Submission: Patients must have sufficient tissue available for the required biology study * Lansky performance status score \>= 50 for patients =\< 16 years of age; Karnofsky performance status score \…