Touch Train Mobility Ware
Try installing Touch Train from Mobility Ware an iPhone app from the App Store.
Attempt once you install it to hit the white pixel in the center of the target.
One thing with it being an iPhone app is it will run in a smaller frame unless you hit the 2X. This should allow an almost precise test as to whether or not your iPad is not functioning correctly on touch calibration.
I would assume once you enlarge the app using 2X the center white pixel will be larger than normal, making it easier to touch. This way you can tell if its actually the way you tap or if it's the digitizer of the iPad itself.
Once you try that you should have a good idea what to tell Apple Service.
PS The app is free...