We define the degenerate two boundary affine Hecke-Clifford algebra Hd, and show it admits a well-defined q(n)-linear action on the tensor space M⊗N⊗V⊗d, where V is the natural module for q(n), and M,N are arbitrary modules for q(n), the Lie superalgebra of Type Q. When M and N are irreducible highest weight modules parametrized by a staircase partition and a single row, respectively, this action factors through a quotient of Hd. Our second goal is to directly construct modules for this quotient, Hdp, using combinatorial tools such as shifted tableaux and the Bratteli graph. These modules belong to a family of modules which we call calibrated. Using the relations in Hdp, we also classifiy a specific class of calibrated modules. This result provides connection to a Schur-Weyl type duality: the irreducible summands of M⊗N⊗V⊗d coincide with the combinatorial construction.