  We describe how certain cyclotomic Nazarov-Wenzl algebras occur as
endomorphism rings of projective modules in a parabolic version of BGG category
O of type $D$. Furthermore we study a family of subalgebras of these
endomorphism rings which exhibit similar behaviour to the family of Brauer
algebras even when they are not semisimple. The translation functors on this
parabolic category O are studied and proven to yield a categorification of a
coideal subalgebra of the general linear Lie algebra. Finally this is put into
the context of categorifying skew Howe duality for these subalgebras.
