What you are seeing would seem to be normal operation. Probably because of errors made by the user or reaction of the touchscreen during certain types to touchscreen activities. It only takes a short time for the screen to react to the double touch, are you waiting a short time before the first double click and the second double click? Does your double click work every time you use it and you don't need to repeat.
A mouse has an adjustment for the double click speed. Does your system have that same type of timing adjustment available for the touchscreen. I would test mine, but it is not currently available.