We investigate the dynamics of chiral microparticles in a dual-beam optical trap. The chiral particles have the structure of spherical chiral microresonators, with a reflectance deriving from the supramolecular helicoidal arrangement. Due to the strong asymmetric response of the particles to light with a specific helicity and wavelength, their trapping position and rotational frequency can be controlled by proper combination of the polarization state of the two light beams. Here symmetric and asymmetric polarization configurations of dual- interfering beam traps have been investigated. Based on the polarization controlled asymmetric transmission of the chiral particles, a tunable wash-board potential is created enabling the control of the trapping position along the beams axis. Asymmetric configurations display polarization controlled rotation of the trapped particles. Optical binding of rotating particles exhibits a complex dynamics.