In my reading, the "as" here should be interpreted as a conjunction that shows comparison. In this case, the "power" and "loving authority" are being compared because the author is saying that they are essentially the same thing. "Loving authority" is portrayed as a concrete showing of the more abstract concept of "power." This particular use of the word "as" is not something that people agree on or necessarily even understand, even if they are natives and interested in grammar. There are other online discussions on this exact sentence! The concept that "as" is a relative pronoun seems strange to me because I don't see the pattern that other relative pronouns follow. Mainly, "represented" here seems to be an adjective describing "power." But a relative clause would need a verb. (You could say, "parents' power, which is represented.") But the power is being represented, not representing something, so I don't believe "as" could be a relative pronoun taking the place of "power."

'as' doesn't really modify anything here, but yes, it references "parents' power'