How long can you get away without the kid?
With 9 days you should be able to keep her happy even if you're missing for 2 in Kalalau in the middle of your trip.
At a minimum the volcano hike can definitely be for couples...
Probably 10 days max. Maybe something like this:
Leave Sun 8/11
Kalalau Mon and Tue, return Wed am.
Have rest of Wed and most of Thu to ourselves, then 2 day shabbos.
Fly to the Big Island Sun am, then shoot the volcano into the night.
Ret. Mon pm or tue am.
That means a 9-10 day trip, 3-3.5 days instructing, 3-3.5 days travel and shabbos, and 2-2.5 days for ourselves.
Or maybe we could do this backwards, fist the volcano and then Kauai, it may work out better. I'll have to check into that after work.
I'll discuss it with my wife later, but I'm hopeful
.