I don't know what story this is from or what is really happening; however, from what I can tell, the author uses the phrase "the annals of parental vigilance" to heavily imply that Daisy's parents are extremely rigid in how they raise her, in an orthodox fashion. "Annals" is defined as yearly record keeping, and "parental vigilance" means that the mother is one that is always watching and correcting her child (from what I can tell.
