I don't see any "Avoid" function in FreeDrive or MapMonkey, so I guess Destinator doesn't support it. Mappoint does support this function, simply click and drag to select a square on the map and click Tools>Avoid Area. You can resize the area selected at any time, however you need to recalculate the route for the changes to be taken into account.
The Destinator PC frontends allow you to import POI locations. Mappoint also. iGuidance currently does not. I wondered about using MapPoint minimised to deal with POI, and run iGuidance on top for map display and routing.