Replacement dongles are covered under Warranty which is found here or you can do a search for the right Xbox dongle on sites such as Ebay to buy them separately but is not fully recommended as you may come across dodgy sellers. You may want to search around the area where your kids was changing the Xbox consoles first before you use the warranty page in case it might've fallen down somewhere as sometimes these can be easily misplaced or have been underneath something. Here's some pics of the dongles themselves for either Xbox platform if you want to know exactly what you want to look for:
Xbox 360 Dongle
Xbox One Dongle
Good luck on finding the dongle that your kids has lost or obtaining an replacement dongle for your console.