  We study the effect of the coupling between the hole $s$ shell of one quantum
dot and the $p$ shell in the other dot forming a quantum dot molecule on the
spin relaxation between the sublevels of the hole $s$ state. Using an effective
model that captures the spin-orbit effects in the $p$ shell irrespective of
their origin, we show that the strong spin mixing in the $p$ shell can be
transferred to the $s$ shell of the other dot, leading to enhanced spin
relaxation in a certain energy range around the $s$-$p$ resonance if the dots
are misaligned and the magnetic field is tilted from the sample plane.
