pushing the directional in the direction you want to swing doesn't require stopping or using R or XR, as it's just changing direction. You just push slowly in the direction you want to move the swinging action, and it will move.
I think on the Gamecube version, you had to stop first, to change direction. Not necessary on the Wii U version, if you use the Gamepad as controller. Not sure if that's also true with the Pro Controller.
But you do have to use XR to stop, which is only necessary if you need to climb the rope completely, or get somewhat higher or lower, for a better jump distance. You have to stop first, and R won't stop the rope from swinging, when using the Wii U Gamepad.