I've Island-Hopped in Hawaii many times, but I wouldn't consider your idea of doing it on the same day. By the time you get through the airport, get a rental car (which you will NEED to have), then drive to where you want to visit, your day is already seriously used. Visiting the location, then reversing the process to fly back to the other island takes the rest of the day. When you're done, you'll think, "I went through all that extra hassle, just to see THAT?" I'd never do that to myself.
Driving from Kona Airport to Volcano can be done in a few hours, but you'll miss seeing a LOT of cool stuff along the way. The route should not be rushed. Volcano National Park has a lot of other things to see than just the crater. So it takes time.
The Road to Hana down and back is easily much more than a half-day trip. I've driven it several times while staying on Maui, and it's an all-day thing, even on the best of days. The stops along the road are what makes it fun - if you're pushing the clock, you won't be able to enjoy yourself. Add traffic or an accident in front of you, and time stops. I'd never attempt that on a turn-around day like you're thinking.
My strong advice: If you have a Weeks timeshare, and you can't get additional time off to pad the vacation, leave the timeshare a few days early, fly to the other island and stay in a hotel (or wherever) for the remaining nights while you see the thing you want to see, then fly home directly from that second island. It's the only practical way to see and do a second island on your restricted schedule.
Ideally, tie your vacation at the timeshare with a few days on that second island before you get to your timesahre week. That way the other visit is done, and your timeshare week can still happen in a restful way. You're going to Hawaii for relaxation, not to add to your stress.
Dave