If you purchased an account for your child but did not do this from their existing account, you can easily link your billing user account to theirs to make them a sub-user on your account.

Log in to the billing account, and head to the accounts tab. Click your account, and you should see this option:

Select "Add existing user", and type the email address of the user you'd like to link to your account. When you submit, a notification will be sent to that user when they log in next. So, all they need to do is log in and accept your request, and the accounts will successfully link. 

By linking the sub-user to a billing account, the billing user (typically the parent or adult who purchased the account) can access the details and settings for the membership.