We have studied the photodissociation and recombination dynamics of the diatomic anions X(2)(-) and XY(-) designed to mimic I(2)(-) and ICl(-), respectively, by using a one-electron model in size-selected N(2)O clusters. The one-electron model is composed of two nuclei and an extra electron moving in a two-dimensional plane including the two nuclei. The main purpose of this study is to explain the salient features of various dynamical processes of molecular ions in clusters using a simple theoretical model. For heteronuclear diatomic anions, a mass disparity and asymmetric electron affinity between the X and Y atoms lead to different phenomena from the homonuclear case. The XY(-) anion shows efficient recombination for a smaller cluster size due to the effect of collision-mediated energy transfer and an inherent potential wall on excited state at asymptotic region, while the recombination for the X(2)(-) anion is due to rearrangement of solvent configuration and faster nonadiabatic transitions. The results of the present study illustrate the microscopic details of the electronically nonadiabatic processes which control the photodissociation dynamics of molecular ions in clusters.