We study the quantum dynamics in a model system consisting of two electrons and a nucleus which move between two fixed ions in one dimension. The numerically determined wave functions allow for the calculation of time-dependent electron localization functions in the case of parallel spin and of the time-dependent antiparallel spin electron localization functions for antiparallel spin. With the help of these functions, it becomes possible to illustrate how electronic localization is modified through the vibrational wave-packet motion of the nucleus.