Xbox Live Gold on Two Different Consoles

Taken from the official support website:

Profile improvements and changes

Latest console software picture The latest console software includes the following profile improvements and changes:

You can download your Xbox Live profile to multiple consoles. However, you can only sign in to one profile at a time. Your profile is automatically updated on your console and Xbox Live, whenever you sign in or out of your profile. To help keep your account safe, you can choose to require or not require your Microsoft account password on any console, For more information, see Password-protect your Xbox Live profile. If the last time you signed in to your profile you were using a different console, you’ll see a notification of this when you sign in. For more information, see Your gamertag was last signed in on another console. It takes significantly less time to download your profile (called "recover" in previous versions of the console software). https://support.xbox.com/en-US/my-account/manage-gamertag-and-profile/profile-storage-changes

Since this is a three year old post, with enough time the problem fixed itself and now have it saved on every console just only signed in at one time.

I would suggest buying your son a prepaid card. You do have to remember when it runs out and buy another, but they tend to be $10-15 cheaper than buying the same amount of time through Microsoft directly. It's also much easier to stop being a subscriber, since you just don't add more time to the account - no need to figure out how to stop the automatic payments.