Parent 1 had an account for a child. The father of that child applied for insurance coverage for the mutal child from Parent and another child. The father's application was merged with Parent 1 existing account. The father's account was established with his information but parent 1 name was listed on the account and not the father. A letter was sent to the parent 1 at the father's address. Is this HIPAA violation?

Your concern here is that information about the "other child" was sent to "Parent1" - and this "parent1" is not that child's parent, correct?

It depends what was disclosed in the letter that you mentioned. HIPAA covers disclosure of health-related information, but strictly speaking does NOT cover disclosure of the existence of insurance coverage itself. More important that worrying about whether it's a HIPAA violation you should be working with the insurance administrator to get them to straighten out their records.