  We present a detailed study of direct CP violation and branching ratios in
the channels $B^{0,\pm} \to \pi^{+}\pi^{-} V^{0,\pm}$, where $V$ is a vector
meson ($K^{*
  0,\pm}$ or $\rho^{\pm}$). Emphasis is placed upon the important role played
by ${{\rho}^{0}}-{\omega}$ mixing effects in the estimation of the CP-violating
asymmetry parameter, $a_{cp}$, associated with the difference of $B$ and $\bar
B$ decay amplitudes. A thorough study of the helicity amplitudes is presented
as a function of the pion-pion invariant mass. All of the calculations and
simulations considered correspond to channels which will be analyzed at the
LHCb facility.
