In Fifa, special players can be bought in packs, but the contents are only revealed after payment is completed.
The children's father, Thomas Carter, had bought them a single pack for around £8, and had not realised they had seen how he made the purchase.
The Switch has now been confiscated "indefinitely", Mr Carter said.
Nintendo has agreed to a full refund and has removed the purchased players.
While Fifa is published and sold by Electronic Arts, the payments had been made via the family's Nintendo account.