"It scares me to think that it is illegal for the clinic to inform the parents.."
That's not what the Alaska law said.  If the patient agrees, the clinic can tell the parents.  It is when the patient doesn't agree that the Alaska law forces the doctor himself or herself to personally notify the parents, after checking the parents' IDs, that can only be a certain kind of ID.  Then the patient has to wait 2 days before she can get an abortion.  Read the decision.