  In this paper, we study harmonic analysis on the affine Poincar\'e group
$\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain
pseudo-differential operators with operator valued symbols. More precisely, we
study the boundedness properties of pseudo-differential operators on
$\mathcal{P}_{aff}$. We also provide a necessary and sufficient condition on
the operator-valued symbols such that the corresponding pseudo-differential
operators are in the class of Hilbert--Schmidt operators. Consequently, we
obtain a characterization of the trace class pseudo-differential operators on
the Poincar\'e affine group $\mathcal{P}_{aff}$, and provide a trace formula
for these trace class operators. Finally, we study the Wigner transform, and
Weyl transform associated with the operator valued symbol on the Poincar\'e
affine group $\mathcal{P}_{aff}$.
