I have been looking again at my Curved Surface plugin (CSP) to see what might be possible. Essentially I have found what David has described. The path for the extrusion cannot have sharp kinks. The if the paths with two straight lines as described by David are joined with a short fillet, and then by choosing a suitable small diameter cutter then it is possible to get close to the required sharp edge - but it will still be filleted.
I suspect, also, that if you try to break the machining into two parts you will get some over-cutting near the outer-side corner, or some uncut regions depending on where you align the two parts. You might be able to tweak an acceptable result.
Taking another approach however, it might be possible to use the Profile-Side Profile option - assuming that the profile to be cut is (semi)circular, like as shown in the attached image. In this case I have created two edges to be profiled as two polylines aligning them with the top ends of the required semi-circular profile. Then I defined a profile MOP on each with a concave edge profile (only final cuts displayed in the image.) I think that you will get a relatively sharp edge on the outer corner, but the inner corner will be filleted towards the bottom of the profile - though quite sharp near the surface.
Geoff