  A double quantum dot device, connected to two channels that only see each
other through interdot Coulomb repulsion, is analyzed using the numerical
renormalization group technique. By using a two-impurity Anderson model, and
parameter values obtained from experiment [S. Amasha {\it et al.}, Phys. Rev.
Lett. {\bf 110}, 046604 (2013)], it is shown that, by applying a moderate
magnetic field, and adjusting the gate potential of each quantum dot, opposing
spin polarizations are created in each channel. Furthermore, through a well
defined change in the gate potentials, the polarizations can be reversed. This
polarization effect is clearly associated to a spin-orbital Kondo state having
a Kondo peak that originates from spatially separated parts of the device. This
fact opens the exciting possibility of experimentally probing the internal
structure of an SU(2) Kondo state.
