Your allocation of nights looks like a nice trip.

I like to recommend visiting two islands on trips of 10 or more days. Three or more islands in one trip crosses my line of how much schlepping and packing/unpacking I want to do. The Big Island is large enough that you could only spend your time on the sunnier Kona/Waikoloa side without going to the Hilo/Volcano side or you can allocate at least a full day or two days and an overnight for the latter.

Something to keep in mind is that HNL has, by far, the most flights to/from the Mainland and also the most operated by widebodies and lie-flats. When flying inter-island, Hawaiian has some limited code-sharing with some of the major carriers but otherwise is stand-alone for a frequent flyer program and interline and checked baggage perspective. Southwest is it's own stand-alone but doesn't charge for checked bags.