We study a two-stage robust linear program with right-hand side uncertainty and relatively complete recourse. Since the problem is computationally intractable in general, we present an equivalent copositive programming reformulation for which a hierarchy of ``tractable'' conservative approximation is known to exist. In particular, we establish a valuable connection between the approximation obtained using the non-negative cone and affinely adjustable robust counterpart models. An important side product of this work is to identify an equivalent reformulation of the recourse problem that ensures the feasibility of affine adjustments. We demonstrate the performance of this approximation scheme on different operations management problems.