  Motived by the accumulated experimental results on three-body charmed $B$
decays with resonance contributions in Babar, LHCb and Belle (II), we
systematically analyze $B_{(s)} \to D_{(s)} (V \to) P_1 P_2 $ decays with $V$
representing a vector resonance ($\rho, K^*, \omega$ or $\phi$) and $P_{1,2}$
as a light pseudoscalar meson (pion or kaon). The intermediate subprocesses
$B_{(s)} \to D_{(s)} V$ are calculated with the factorization-assisted
topological-amplitude (FAT) approach and the intermediate resonant states $V$
described by the relativistic Breit-Wigner distribution successively decay to
$P_1 P_2$ via strong interaction. Taking all lowest resonance states ($\rho,
K^*, \omega, \phi$) into account, we calculate the branching fractions of these
decay modes as well as the Breit-Wigner-tail effects for $B_{(s)} \to D_{(s)}
(\rho ,\omega \to) KK$. Our results agree with the data by Babar, LHCb and
Belle (II). Among the predictions that are still not observed, there are some
branching ratios of order $10^{-6}-10^{-4}$ which are hopeful to be measured by
LHCb and Belle II. Our approach and the perturbative QCD approach (PQCD) adopt
the compatible theme to deal with the resonance contributions. What's more, our
data for the intermediate two-body charmed $B$-meson decays in FAT approach are
more precise. As a result, our results for branching fractions have smaller
uncertainties, especially for color-suppressed emission diagram dominated
modes.
