Delta just changed their rules to allow bikes as part of baggage allowance, FYI. Also, Seasuckers fit in a bike bag and can go on any car. You could also simply call a flotilla of Ubers and Lyfts to get you and the family/gear to the resort? I was just going to lunch in Kauai and the dude picked me up in a Tundra that could have fit a family of four, luggage and a team’s worth of road bikes.
Also, you should call the resort and see how they can help you out. Transport can be wildly variable depending on which island you are staying on and where the resort is.
Personally I’d pack a board bag S shore swells have been pretty decent this summer.