They were thrown out of the centre after they took out a camera to snap the look on the youngsters' faces when they turned up unexpectedly.
The couple were on a four-day break from their home in Spain and wanted to surprise their family by arriving at the centre, in Fareham, Hants, while they were shopping. But when they went to take a photo, a security guard pounced and ordered them out.
The guard then insisted that cameras were banned because of the risk of a terrorist attack - and barred the bemused couple for life.
Speaking from her home in Malaga, Spain, Mrs Sparshott, 51, said: "I couldn't believe it. I was so shocked. "He said we had committed an act of terrorism. At first I wanted the ground to swallow me up whole because it was so embarrassing - but then I got really angry." Mr Sparshott, 52, added: "Instead of being a nice surprise for our family it turned into a nightmare. I was furious. In these worrying times we understand the need for caution, but surely a quiet word when he first saw us would have stopped all this unpleasantness."