I find that try going in the bend of the lead so if your horse wants to change it will be difficult as he would make himself unbalanced by changing also try do some circles coming of the center line to encourage the bend this has worked with a couple of my horses so I hope it works for you!
Hope this helps
Try to ride a contercanter before entering the line so there is no reason for her to change at all. When she is good with that you can try again to ride the line without it. If that doesn't work try riding around the arena in contercanter do she learns that that's also an possible exercise.