Two Xbox's in the same household

You can't sign into 2 different Xbox Ones with the same console. You would each need your own account (if you don't have one already) and then you would each be able to sign into each console and play separate games.

You need to make each other's consoles the home Xbox using your own account. More info on here about the home xbox setting https://support.xbox.com/en-US/help/hardware-network/console/my-home-xbox

As for discs, you can play the disc on any Xbox One or Series X|S console you want.

You can share between two profiles, you have account A the primary account and account B the new account.

On the first console you have account A, and on the second console add account A make this the home xbox

https://beta.support.xbox.com/search?phrase=home%20xbox

Now add the second profile to that console and now the second account will have access to everything on the primary account to include the xbox gold membership. This way you can play on two separate accounts, even together in the same game.

There is one additional issue and that is having two xbox's on the same network but there is a solution for that.

https://portforward.com/portforward-two-xboxes/default.htm

You would set theirs as your Home and they would set yours as their Home. https://support.xbox.com/en-US/help/hardware-network/console/my-home-xbox

Home Xbox is a fantastic feature to help make this happen, as Leslie mentioned. All content in your account (games, subscriptions, etc.) will be shared to both consoles. Just know that if there is any content (games, DLC, etc.) purchased on your son's account
and not yours, only he will be able to access that content on the Xbox where he is signed in.

Does your son already have his own account? If not, check out this link to set up an account for him under your account: Add a new member
to your family on Xbox One

Let us know if you have any questions!

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Let me know if this solves your problem!