  Binary black hole spin measurements from gravitational wave observations can
reveal the binary's evolutionary history. In particular, the spin orientations
of the component black holes within the orbital plane, $\phi_1$ and $\phi_2$,
can be used to identify binaries caught in the so-called spin-orbit resonances.
In a companion paper, we demonstrate that $\phi_1$ and $\phi_2$ are best
measured near the merger of the two black holes. In this work, we use these
spin measurements to provide the first constraints on the full six-dimensional
spin distribution of merging binary black holes. In particular, we find that
there is a preference for $\Delta \phi = \phi_1 - \phi_2 \sim \pm \pi$ in the
population, which can be a signature of spin-orbit resonances. We also find a
preference for $\phi_1 \sim -\pi/4$ with respect to the line of separation near
merger, which has not been predicted for any astrophysical formation channel.
However, the strength of these preferences depends on our prior choices, and we
are unable to constrain the widths of the $\phi_1$ and $\Delta \phi$
distributions. Therefore, more observations are necessary to confirm the
features we find. Finally, we derive constraints on the distribution of recoil
kicks in the population, and use this to estimate the fraction of merger
remnants retained by globular and nuclear star clusters. We make our spin and
kick population constraints publicly available.
