This study concentrates on a relatively simple model of a mushy layer originally proposed by Amberg & Homsy (1993) and later studied in further detail by Anderson & Worster (1995). We extend this model to the case in which the system is in a state of uniform rotation about the vertical. Of particular interest is to determine how the rotation of the system controls the bifurcating convection with both the oblique-roll planform and the planform of hexagonal symmetry. We find that two-dimensional oblique rolls can be either subcritically or supercritically bifurcating, depending on a pair of parameters (K1/CS, [Tscr]), where K1 measures how the permeability linearly varies with the local solid fraction, CS relates the compositional difference between the liquid and solid phases to the variation of composition throughout the mushy layer, and the Taylor number [Tscr] gives a measure of the local Coriolis acceleration relative to the viscous dissipation in a porous medium. The three-dimensional convection with hexagonal symmetry is found to be transcritical. Furthermore, distorted hexagons with upflow at the centres can be either subcritical or supercritical, depending on the value of the Taylor number [Tscr].