  We discuss the theory and phenomenology of $B_{d,s}\to V(\to M_1M_2)\ell\ell$
decays in the presence of neutral-meson mixing. We derive expressions for the
time-dependent angular distributions for decays into CP eigenstates, and
identify the relevant observables that can be extracted from time-integrated
and time-dependent analyses with or without tagging, with a focus on the
difference between measurements at $B$-factories and hadronic machines. We
construct two observables of interest, which we call $Q_8^-$ and $Q_9$, and
which are theoretically clean at large recoil. We compute these two observables
in the Standard Model, and show that they have good potential for New Physics
searches by considering their sensitivity to benchmark New Physics scenarios
consistent with current $b\to s\ell\ell$ data. These results apply to decays
such as $B_d\to K^*(\to K_S\pi^0)\ell\ell$, $B_s\to \phi (\to K_SK_L)\ell\ell$
and $B_s\to \phi(\to K^+K^-)\ell\ell$.
