You have two choices:
(1) Create a flipped brain for one condition, then do a voxelwise test of the positive and negative stimuli. This assumes that the flip aligns homologous regions on each side.
(2) Draw regions in the left and right hemispheres, extract the contrast values in the ROIs, then test for an interaction between hemisphere and valance.
You must explicitly test the hemisphere interaction in some way to draw the conclusion you have hypothesized. Seeing activation in one hemisphere and not the other doesn't allow you to say the positive/negative differences are different between hemispheres.