We went to Kauai a couple of years ago. Services on the island are a little on the scarce side. I think there's one baby gear rental place but if you're not happy with what they provide you'll be really stuck and you'll have to send someone to Walmart (which is NOT near the airport) to buy new seats.
Also, I don't know how we would have coped with the flight if we didn't have our car seat on board. Granted, my daughter was an infant at the time, but she's 2 now and there is absolutely no way you could pay me enough to take a flight that long without a car seat to hold her in place.
So, basically, I think you really really need to bring car seats both ways. If you post your kids' height, weight, and whether they ride RF or FF we could easily suggest some good lightweight plane-friendly budget options for you. I totally get not wanting to take an Advocate on the plane. That thing is huge.