Just because HA is pointing the finger at DL does not mean that your thread title is accurate. It could be exactly the reverse. Of course HA can't issue a refund, HA is not the ticketing carrier.

There are three options:
1. Forget about it for the moment. This flight is blocked at 40 minutes with about 20 minutes in the air. Let your wife sit in F and you can suffer in steerage. When you return, ask DL to refund the fare difference for F over Y and then initiate a DOT complaint and chargeback if you do not promptly receive it.

2. Call DL and have them reticket in F. But, you will have to accept the Y seat and priority standby for F as there are no F seats available, or shift at least one of you to a later flight.

3. Get DL & HA on a thee-way call and sort it out with both on the line. But, same problem, no space in F on the preferred flight.

It is water under the bridge for OP, but the wife's HA segment is on a separate ticket issued by DL. That is always risky and there is almost never a reason to do that. In this situation, simply go on the HA website and purchase the HNL-OGG ticket. Absent some real mess, OP would have had an F ticket for his wife issued by the operating carrier.

Also worth noting for OP that his wife's HNL-OGG ticket is separate and therefore she is not connecting at HNL. If the inbound DL is delayed and she no shows for the HA ticket, it will be cancelled and will have whatever value it retains under its specific fare rules. A walk-up ticket is $64, so it is not the end of the world, but it is just something to keep in mind.