 This randomized phase II trial studies how well cisplatin and gemcitabine hydrochloride with or without ATR kinase inhibitor VX-970 works in treating patients with urothelial cancer that has spread to other places in the body. Drugs used in chemotherapy, such as cisplatin and gemcitabine hydrochloride, 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. ATR kinase inhibitor VX-970 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known if cisplatin and gemcitabine hydrochloride work better alone or with ATR kinase inhibitor VX-970 in treating patients with urothelial cancer. 