  We describe, in an algebraic way, the $\kappa$-deformed extended Snyder
models, that depend on three parameters $\beta, \kappa$ and $\lambda$, which in
a suitable algebra basis are described by the de Sitter algebras ${o}(1,N)$.
The commutation relations of the algebra contain a parameter $\lambda$, which
is used for the calculations of perturbative expansions. For such
$\kappa$-deformed extended Snyder models we consider the Heisenberg double with
dual generalized momenta sector, and provide the respective generalized quantum
phase space depending on three parameters mentioned above. Further, we study
for these models an alternative Heisenberg double, with the algebra of
functions on de Sitter group. In both cases we calculate the formulae for the
cross commutation relations between generalized coordinate and momenta sectors,
at linear order in $\lambda$. We demonstrate that in the commutators of quantum
space-time coordinates and momenta of the quantum-deformed Heisenberg algebra
the terms generated by $\kappa$-deformation are dominating over
$\beta$-dependent ones for small values of $\lambda$.
