The ability to control the spin-transport properties of a molecule bridging conducting electrodes is of paramount importance to molecular spintronics. Quantum interference can play an important role in allowing or forbidding electrons from passing through a system. In this work, the spin-transport properties of a polyacetylene chain bridging zigzag graphene nanoribbons (ZGNRs) are studied with nonequilibrium Greens function calculations performed within the density functional theory framework (NEGF-DFT). ZGNR electrodes have inherent spin polarization along their edges, which causes a splitting between the properties of spin-up and spin-down electrons in these systems. Upon adding an imidazole donor group and a pyridine acceptor group to the polyacetylene chain, this causes destructive interference features in the electron transmission spectrum. Particularly, the donor group causes a large antiresonance dip in transmission at the Fermi energy EF of the electrodes. The application of a gate is investigated and found to provide control over the energy position of this feature making it possible to turn this phenomenon on and off. The currentvoltage (IV) characteristics of this system are also calculated, showing near ohmic scaling for spin-up but negative differential resistance (NDR) for spin-down.