Synoptic searches for the optical counterpart to a binary neutron star (BNS) or neutron star-black hole (NSBH) merger can pose significant challenges towards the discovery of kilonovae and performing multi-messenger science. In this work, we describe the advantage of a global multi-telescope network towards this end, with a particular focus on the key and complementary role the Dark Energy Camera (DECam) plays in multi-facility follow- up. We describe the Global Relay of Observatories Watching Transients Happen (GROWTH) Target-of-Opportunity (ToO) Marshal, a common web application we built to ingest events, plan observations, search for transient candidates, and retrieve performance summary statistics for all of the telescopes in our network. Our infrastructure enabled us to conduct observations of two events during O3a, S190426c and S190510g. Furthermore, our analysis of deep DECam observations of S190814bv conducted by the DESGW team, and access to a variety of global follow-up facilities allowed us to place meaningful constraints on the parameters of the kilonova and the merging binary. We emphasize the importance of a global telescope network in conjunction with a power telescope like DECam in performing searches for the counterparts to gravitational-wave sources.