Forget the HI-LAX family issue. OP and his wife can switch seats. She simply takes the F seat and he takes the Y seat. Both seats are occupied and both passengers are onboard. While it is technically true that DL could require only the ticketed pax to sit in the F seat, that isn't done.

As to baggage, OP apparently did not check the e-ticket receipts or he would have seen the baggage charge discrepancy, e.g., a difference between MCO-HNL and HNL-OGG.

While it is irrelevant to this particular circumstance, the DOT rule looks to the allowance and practice of the marketing carrier of the first segment of the ticket and applies that to all subsequent segments, including the return.

If the marketing carrier chooses to apply the old IATA MSC rule, then that is the rule that applies and that might cause a change in the allowance. But, for ease of reference, none of the US carriers apply the old MSC rule so it is irrelevant to any ticket where the marketing carrier is a US carrier. Here, it makes no difference as DL is both the marketing carrier of the first segment and the MSC carrier.

OP avoids this entire mess by checking luggage on his cash F ticket. HA applies the DL F allowance to the departure from OGG (but not any allowances for status).