  Drinfeld orbifold algebras deform skew group algebras in polynomial degree at
most one and hence encompass graded Hecke algebras, and in particular
symplectic reflection algebras and rational Cherednik algebras. We introduce
parametrized families of Drinfeld orbifold algebras for symmetric groups acting
on doubled representations that generalize rational Cherednik algebras by
deforming in degree one. We characterize rich families of maps recording
commutator relations with their linear parts supported only on and only off the
identity when the symmetric group acts on the natural permutation
representation plus its dual. This produces degree-one versions of
$\mathfrak{gl}_n$-type rational Cherednik algebras. When the symmetric group
acts on the standard irreducible reflection representation plus its dual there
are no degree-one Lie orbifold algebra maps, but there is a three-parameter
family of Drinfeld orbifold algebras arising from maps supported only off the
identity. These provide degree-one generalizations of the
$\mathfrak{sl}_n$-type rational Cherednik algebras $H_{0,c}$.
