If you have an existing route in RWGPS, select edit, and you can add to it, subtract from it, move control points etc. and then save it as a new route.
If you want to move a piece of a route, first click on Add/Remove control points, delete all the points on the section you wish to move, then click on ADD/Remove again and drag the red line to where you want it to go, which will leave a control point where you let go of the mouse button. Grab the red line a little further along and drag it to where you want it.
When placing a control point, don't do it at an or near an intersection.