  We study deformations of the Howe dual pairs
$(\mathrm{U}(n),\mathfrak{u}(1,1))$ and $(\mathrm{U}(n),\mathfrak{u}(2|1))$ to
the context of a rational Cherednik algebra $H_{1,c}(G,E)$ associated with a
real reflection group $G$ acting on a real vector space $E$ of even dimension.
For each pair, we show that the Lie (super)algebra structure of one partner is
preserved under the deformation, which leads to a multiplicity-free
decomposition of the standard module or its tensor product with a spinor space.
For the case where $E$ is two-dimensional and $G$ is a dihedral group, we
provide complete descriptions for the deformed pair and the relevant
joint-decomposition.
