You need to have your daughter remove the account she added to your iPad.
Where are you seeing the strangers Apple ID? Check the App Store and iTunes Store to see if there are any updates for apps/purchases. A request for another Apple ID password is often caused by updates to apps/purchases that were made when using the other ID. Those purchases are tied to the other ID and can't be transferred. One option is to delete the apps/purchases made by the other ID and download them using the new ID if desired. If necessary, check your purchases history to see which apps/purchases weren’t made by the current ID.
Purchase History Review.