  We use braided groups to introduce a theory of $*$-structures on general
inhomogeneous quantum groups, which we formulate as {\em quasi-$*$} Hopf
algebras. This allows the construction of the tensor product of unitary
representations up to a quantum cocycle isomorphism, which is a novel feature
of the inhomogeneous case. Examples include $q$-Poincar\'e quantum group
enveloping algebras in $R$-matrix form appropriate to the previous
$q$-Euclidean and $q$-Minkowski spacetime algebras $R_{21}x_1x_2=x_2x_1R$ and
$R_{21}u_1Ru_2=u_2R_{21}u_1R$. We obtain unitarity of the fundamental
differential representations. We show further that the Euclidean and Minkowski
Poincar\'e quantum groups are twisting equivalent by a another quantum cocycle.
