From the viewpoint of oblate-prolate symmetry and its breaking, we adopt the quadrupole collective Hamiltonian to study the dynamics of triaxial deformation in shape coexistence phenomena. It accommodates the axially symmetric rotor model, the gamma-unstable model, the rigid triaxial rotor model, and an ideal situation for the oblate-prolate shape coexistence as particular cases. Numerical solutions of this model yield a number of interesting suggestions. (1) The relative energy of the excited 0(+) state can be a signature of the potential shape along the gamma direction. (2) Specific E2 transition probabilities are sensitive to the breaking of the oblate-prolate symmetry. (3) Nuclear rotation may induce the localization of collective wave functions in the (beta, gamma) deformation space.