The Forge accounts and the Foundry players are completely independent. The Foundry ‘logins’ you create are just players within that specific world itself, If you had two worlds in Foundry, even a login on world A would not work if you launched world B. The Forge account on the other hand is unique and associated with one individual per their email address, and in your case for example, it’s what you used to subscribe and configure your game URL and it’s where you have your dashboard which gives you access to all the other games you were invited on.
If The Forge says that the account already exists when you tried to sign up, that would most likely refer to the email address used for signing up, and I assumed you entered your own email address.
Trying to access the direct URL of your Foundry game without first logging into The Forge and using the invitation link will not work, as by default all games are set to Private. You can read more about Public and Private games here :
Though it is not recommended to set your game to public, for security and privacy reasons, in the case of your nephew, if they are under 13 years old, then due to COPA (Children Online Privacy Act) laws, they can’t create a Forge account, and that’s what the concept of ‘public games’ was created for.
Hopefully that helps make it clearer.