As I understand the rule - since the outbound is a stopover and not a connection, flight to HNL should be no charge as F cabin, but to OGG should be a charge, though not sure if, it is UA-coded codeshare flight, that would go by Island Air or UA fees. If it is the Island Air flight number, definitely Island Air fee.

Since the return is a connection, not a stopover, UA F allowance should apply for entire itinerary to LAX.