This randomized phase II/III trial studies how well pazopanib, when combined with chemotherapy and radiation therapy or radiation therapy alone, work in the treatment of patients with newly diagnosed non-rhabdomyosarcoma soft tissue sarcomas that can eventually be removed by surgery. Radiation therapy uses high energy x-rays to kill tumor cells. Drugs used in chemotherapy, such as ifosfamide and doxorubicin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Pazopanib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether these therapies can be safely combined and if they work better when given together in treating patients with non-rhabdomyosarcoma soft tissue sarcomas.