XBOX Live requires parent account to login before child account can access it.

It sounds like the Xbox Live Gold subscription is on your account and not your sons. Hopefully, you are using an Xbox One rather than an Xbox 360. You need to sign in on the Xbox One with the account that has the subscription and make that Xbox the Home
console. Once you do that, any account that uses that console can access most Gold subscription features without your account needing to be signed in.

Xbox Live subscriptions are attached to the account rather than the console unless you make that console the Home console.

https://support.xbox.com/help/hardware-network/console/my-home-xbox

Is there any parental restrictions on your console ?

If you did not create a Live account that is not over 18 years old, it is unfortunately impossible to COMPLETELY remove the parental controls on the Xbox, however, it is possible to almost completely turn them off. If you have access to the 'parent' account
of the child's account on the Xbox 360 and you have your own Xbox Live Gamertag, you can login using your Windows Live account on Xbox.com and change parental control settings.

If the "Child" account has reached the age of 18, then you need to sign into the "Parent" account and follow these steps to convert the account to an "Adult" account:

Go to My Xbox, and open your profile.

Select Manage Account.

Select Promote Child Account.

Follow the required steps.

If the "Child" account is NOT atleast 18 years old then this is how to modify the Parental Control settings (Note: You can NOT completely disable Parental Controls, games that have ratings above the neccesary age can NOT be downloaded on the "Child"account):

Sign in using the "Child" account's Live email address and password.

Click on the gamertag in the upper right hand corner of the site.

Click the Manage Profile button.

Under the Gamer Profile heading, choose "Family Settings".

It will now ask to sign in as the "Parent" account.

After signing in, you can change the Parental Control limitations.

When done, click the save button at the bottom of the page.

Problem:

You see the following error and message when you try to sign in to Xbox Live using a child account:

Before you can sign in here, you'll need to sign in at Xbox.com.

An adult will also need to sign in so they can give permission.

Code: 83118853

This means that the parent account must provide permission for each associated child account (under age 13) before the child can access Xbox Live

Solution:

To resolve this issue, have the child account sign in to Xbox.com. Then, when prompted, the parent account associated with the child account should sign in to Xbox.com and give permission for the child account to sign in to Xbox Live.

If you keep experiencing the problem, contact Xbox Support.

Error 83118853 occurs when you try to sign in to Xbox Live using a child account

You see the following error and message when you try to sign in to Xbox Live using a child account:

Before you can sign in here, you'll need to sign in at Xbox.com.

An adult will also need to sign in so they can give permission.

Code: 83118853

This means that the parent account must provide permission for each associated child account (under age 13) before the child can access Xbox Live.

Starting today some U.S. child accounts (under 13) will no longer be able to log into their Xbox 360 (in some instances Xbox Music on Windows 8 or 8.1) until a parent verifies the child account on Xbox.com. All new child accounts will be required to verify
that an adult is giving permission to a child to create a new Xbox Live account.

As part of our continued effort to provide the best possible experience for our customers around the world, Microsoft issued a global update. In connection with this update and the recent launch of Xbox One, Microsoft reviewed Xbox Live’s processes for online
account creation and use (including existing accounts) by children (under 13) to ensure ongoing compliance with the recently amended Children’s Online Privacy Protection Act (COPPA). COPPA requires that prior to gathering personal information from a child
(under 13), providers of online services obtain verifiable parental consent from the child’s parent. Microsoft and Xbox Live comply with the COPPA regarding online account creation for children under age 13. The most common method allowed by COPPA for gathering
parental consent is charging a small amount to the parent’s credit card. We charge 50 cents for this verification. These charges aren’t refundable

Yes you can. You need to log in as the parent that currently has control over the account. From there you can remove the child from the family. Once this has been completed the Childs account will be required to be attached to another parent account before
they can do anything.

I'm not sure but it may do this the instant the child account is removed from the parent account, or the next time the child logs in.