In vehicle-to-vehicle (V2V) channels, such roadside scatterers (RSSs) as houses, buildings, trees, and many more, play a crucial role in the determination of the Doppler power spectral density (DPSD) characteristics. However, the relevant research results are scarce due to the lack of computationally tractable analytic DPSD solutions. To fill this gap, we investigate an indirect method for the DPSD analysis of a generic two-dimensional (2D) RSS model for V2V channels. The indirect method, based on the Hoeher's theorem, employs successive transformations of random variables to obtain the DPSD. Compared to the conventional methods, leading to impractical multiple integral solutions, our method yields a single integral-form, more useful for analytic studies, model validation/parameter estimation, and fading simulator design. Using the new DPSD solution, the impact of different RSS layouts on the DPSD characteristics is further investigated, and several new insights are provided. The joint probability density function (PDF) of angle-of-departure and angle-of-arrival (AoA) and the joint Doppler-AoA PDF are newly presented in closed-forms and analyzed with respect to the DPSD shape. Comparisons with the DPSDs measured in highway and \FB{urban canyon} environments demonstrate not only the validity of the generic 2D RSS model, but also the significant contribution of RSSs to V2V channels.