We present Dalitz plot analyses for the decays of B mesons to D⁻D⁰K⁺ and D̅⁰D⁰K⁺. 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{₋₇}⁺¹⁴ MeV/c² and of the width Γ(D*{s1} (2700)⁺) = 127{₋₁₉}⁺²⁴ MeV, including statistical and systematic uncertainties. In addition, we observe an enhancement in the D⁰K⁺ invariant mass around 2350-2500 MeV/c² in both decays B⁰ → D⁻D⁰K⁺ and B⁺ → D̅⁰D⁰K⁺, which we are not able to interpret. The results are based on 429 fb⁻¹ of data containing 471 x10⁶ BB̅ pairs collected at the ϒ(4S) resonance with the BABAR detector at the SLAC National Accelerator Laboratory.