A dynamical model combining an extended diatomics-in-molecules approach with the inclusion of the spin-orbit coupling and the mean-field dynamics method has been developed for rare-gas cluster cations, Rg(n)(+), and employed in simulations of the photodissociation dynamics of argon, krypton, and xenon singly charged trimers. As the first step, total kinetic energies deposited in the photofragments are calculated for all the three rare gases and for a wide range of photon energies, and compared with available experimental data. A very good agreement between experiment and theory is reached, including a plausible theoretical explanation for an abrupt change in the total kinetic energy of photofragments at about 2.5 eV of photon energy, which was recently observed experimentally for Xe(3)(+) (and also, but less clearly for Ar(3)(+)).