Here are a couple of tips: 1) Touch firmly (the screen is not hyper sensitive by design, which overall makes for better use in airplanes...but does have drawbacks) 2) Try using your fingernail. or 3) You can use a styles, back of a ball point pen, etc, to improve touch accuracy.
If these tips don't help you can use the alternative method to modify your route: 1) Tap your desired waypoint, 2) Touch "Option" on the resulting popup, then 3) Touch "Add Waypoint Here".
Thanks!
Walter