  We consider the deformed versions of the classical Howe dual pairs
$(O(r),\mathfrak{s}\mathfrak{l}(2))$ and
$(O(r),\mathfrak{s}\mathfrak{p}\mathfrak{o}(2|2))$ in the context of a rational
Cherednik algebra $H_c=H_c(W,\mathfrak{h})$ associated to a finite Coxeter
group $W$ at the parameters $c$ and $t=1$. For the first pair, we compute the
centraliser of the well-known copy of
$\mathfrak{s}\cong\mathfrak{s}\mathfrak{l}(2)$ inside $H_c$. For the second
pair, we show that the classical copy of
$\mathfrak{g}\cong\mathfrak{s}\mathfrak{p}\mathfrak{o}(2|2)$ inside the
Weyl-Clifford algebra $\mathcal{W}\otimes\mathcal{C}$ deforms to a Lie
superalgebra inside $H_c\otimes\mathcal{C}$ and compute its centraliser
algebra. For a generic parameter $c$ such that the standard $H_c$-module is
unitary, we compute the joint $((H_c)^{\mathfrak{s}},\mathfrak{s})$- and
$((H_c\otimes\mathcal{C})^{\mathfrak{g}},\mathfrak{g})$-decompositions of the
relevant modules.
