This is more than likely a problem with Routis not getting along with your usb-serial driver software. (I'm assuming your gps mouse is usb.) Since the other apps you tried work, your gps is OK. Make sure you are running with the same port settings for both the mouse and for Routis.
There have been similar problems with the Earthmate gps. Read about it here.
If all else fails, think about getting GPSGate.
Some gps software will only calculate your heading when you're moving. When stopped, your heading will fluctuate. Routis doesn't care about the heading, only that you are past your waypoint, before it will tell you to turn around.