The youngsters were at the Lizard Point Holiday Park near Mullion, Cornwall, on Sunday, where they went from the function room into the amusement arcade together.
The man shouted for the woman to let go of the children, which she did, and the children were then taken back to their families, unharmed.
Officers are now appealing for witnesses to trace the woman, who was said to have been wearing a bright yellow top.
With activities such as archery and an outdoor gym trail, it attracts families with young children to stay in its 32 caravans or bungalows.
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