  We present Dalitz plot analyses for the decays of $B$ mesons to $D^-D^0K^+$
and $\overline{D}^0D^0K^+$. [Charge conjugate reactions are implicitly assumed
throughout.] We report the observation of the $D^*_{s1}(2700)^+$ resonance in
these two channels and obtain measurements of the mass $M(D^*_{s1}(2700)^+) =
2699^{+14}_{-7}$ MeV/$c^2$ and of the width $\Gamma(D^*_{s1}(2700)^+) =
127^{+24}_{-19}$ MeV, including statistical and systematic uncertainties. In
addition, we observe an enhancement in the $D^0K^+$ invariant mass around
2350--2500 MeV/$c^2$ in both decays $B^0 \to D^-D^0K^+$ and $B^+ \to
\overline{D}^0D^0K^+$, which we are not able to interpret. The results are
based on 429 $fb^{-1}$ of data containing $471\times 10^6$ $B\overline{B}$
pairs collected at the $\Upsilon(4S)$ resonance with the BaBar detector at the
SLAC National Accelerator Laboratory.
