Medication refill requests can only be made for medications visible on the Patient Portal. If a medication is set to Clinical Staff Only or higher, it is not available for the parent to see or request a refill. In addition, the client can turn off the Portal Feature for "Allow Med Refill Requests". This will prohibit the link to appear on any Patient Portal account.
OP sets all defaults to share all information. Any individual decisions by Practice-users to restrict information sharing (access, use, or exchange) are the responsibility of the Practice in the implementation of its 21st Century Cures Act Information Blocking policies and procedures for its Practice and patients.