The dynamics of a two-dimensional shell model with a double-well potential in the core-shell interaction is simulated by means of molecular-dynamics techniques. Snapshots of the lattice displacement pattern reveal the presence of precursor regions in the high-temperature phase, while in the low-temperature phase the dynamical structure factor exhibits a quasielastic component in addition to the ferroelectric soft-mode peak. On the other hand, the local dynamics of particles are characterized by two different time scales corresponding to the coexistence of interwell and intrawell motions. In the vicinity of the structural-phase-transition temperature a crossover from a displacive to an order-disorder transition is observed, which may explain the experimentally observed discrepancies of the nature of the phase transition.