  We establish new properties of inhomogeneous spin $q$-Whittaker polynomials,
which are symmetric polynomials generalizing $t=0$ Macdonald polynomials. We
show that these polynomials are defined in terms of a vertex model, whose
weights come not from an $R$-matrix, as is often the case, but from other
intertwining operators of $U'_q(\hat{\mathfrak{sl}}_2)$-modules. Using this
construction, we are able to prove a Cauchy-type identity for inhomogeneous
spin $q$-Whittaker polynomials in full generality. Moreover, we are able to
characterize spin $q$-Whittaker polynomials in terms of vanishing at certain
points, and we find interpolation analogues of $q$-Whittaker and elementary
symmetric polynomials.
