We report detailed calculations of the quantum wavepacket dynamics of Cl-O-O-Cl, which serves as a prototype molecule for the stereomutation dynamics of an axially chiral molecule. We include the effects both from electroweak parity violation and from the interaction with a coherent monochromatic laser field. We use the quasiadiabatic channel reaction path Hamiltonian approach to approximately solve the six-dimensional Schrodinger equation describing the vibrational motion, including rotation by an effective Hamiltonian. We calculate time-dependent wave functions based on the time-dependent Schrodinger equation. We study stereomutation dynamics due to tunneling motion and laser-induced population transfer and show results on efficient methods for selectively populating single molecular states in chiral molecules by frequency-odulated laser pulses. We also discuss laser-induced stereomutation (LISM) and a process that may be called resonance Raman induced stereomutation (RRISM). The results are discussed in relation to current experimental attempts to measure the parity violating energy difference Delta E-pv between the enantiomers of chiral molecules. Furthermore, we show detailed quantitative simulations of a selection of well-defined parity levels in chiral molecules ("parity isomers") that form the basis of a possible measurement of Delta E-pv by the time evolution of parity.