By employing a newly developed nonadiabatic dynamical simulation method, which is a combination of classical molecular dynamics and the adaptive time-dependent density matrix renormalization group, we investigate the dynamics of charge carrier transitions in trans-polyacetylene (PA) with the inclusion of both electron-phonon and electron-electron interactions. The calculations are performed within a modified Su-Schrieffer-Heeger model in which electron-electron interactions are taken into account via the combination with extended Hubbard model (EHM). We find that removing an electron from a trans-PA chain bearing a positively charged polaron leads to the formation of a pair of charged solitons. Furthermore, we study the effect of electron-electron interactions on such charge carrier transitions in trans-PA. Our results show that increasing the on-site Coulomb interaction and the nearest-neighbor Coulomb repulsion will not change the qualitative behavior of the transition from a polaron to a soliton pair in the evolution process but will quantitatively reduce the moving velocities of the both formed solitons significantly and change the conditions for the soliton collisions.