Vehicular ad hoc networks (VANETs) are able to facilitate data exchange among vehicles and provide diverse data services. The benefits of cooperative communications are such as to make it a proper idea to improve the achievable rate and diversity in VANETs. We investigate a dual-hop relay vehicular network with different transmit powers in vehicles on non-uniform shadowed double Nakagami-m fading channels in the presence of non-uniform co-channel interferers. In this paper, we investigate the diversity-multiplexing tradeoff (DMT) in such a network for three different schemes, namely, dynamic decode and forward (DDF), dynamic quantize map and forward and static quantize map and forward and prove that the DDF strategy has the optimal DMT. Also, the optimal listening and transmitting time of vehicles in various strategies as a function of the channel conditions in vehicles are determined. Finally, we extend our results to a general multi-hop relay vehicular network model with multiple half-duplex relay terminals and different average SNRs over links.