This phase III trial compares the safety and effect of adding vinorelbine to vincristine, dactinomycin, and cyclophosphamide (VAC) for the treatment of patients with high risk rhabdomyosarcoma (RMS). High risk refers to cancer that is likely to recur (come back) after treatment or spread to other parts of the body. This study will also examine if adding maintenance therapy after VAC therapy, with or without vinorelbine, will help get rid of the cancer and/or lower the chance that the cancer comes back. Vinorelbine and vincristine are in a class of medications called vinca alkaloids. Dactinomycin is a type of antibiotic that is only used in cancer chemotherapy. Cyclophosphamide is in a class of medications called alkylating agents. Vinorelbine, vincristine, dactinomycin and cyclophosphamide are chemotherapy medications that work by slowing or stopping the growth of cancer cells in the body. This trial may have the potential to eliminate rhabdomyosarcoma for a long time or for the rest of patient's life.