We consider the practical feasibility of using the direct, electric dipole-dipole interaction between cotrapped molecular ions for robust quantum logic without the need for static polarizing fields. The use of oscillating dipole moments, as opposed to static electric dipoles, dynamically decouples the dipoles from laboratory fields, including the electric fields of the trap itself. Further, this implementation does not require the quantum control of motion, potentially removing a major roadblock to ion trap quantum computing scalability. Since the polarizing field is electromagnetic radiation, even pairs of states with splittings in the THz regime can be fully polarized.