I have just checked the websites for Hawaiian and Island, and their luggage charges are considerably less than United has now informed me I have to pay. I therefore assume it is United charging me, not Hawaiian or Island.
As I mentioned, the itinerary clearly states these are codeshares. All I know is I logged on, booked all four flights on Continental (as it was then) website, got one booking confirmation, one eticket number, and it states the two island hops are codeshares. These are quite definitely all on one ticket.
There was no mention of charges for luggage until the latest change by United (and as I say, it was the Hawaiian flight that had changed this time)