OP here! I finally have my report of how this all went.
We stayed at Aulani for 7 days last week, one day we did a day trip to the big island. Thanks to the tips here, it was amazing. We didn't book any tours and the rental car was very cheap (
Avis < $50) and it was the very easiest rental pickup drop-off ever, it took almost no time.
Here was our day:
6am flight from HNL (4 of us travelling, no bags)
7am land Hilo (landed a little early, so maybe 6:50)
7:11 already had rental car, this was so fast.
8am-11:30 am Volcano National Park, we first parked at Kilauea Iki Overlook, got some nice sights from above as we walked towards Thurston Lava tube, after walking through the tube, we hiked down to the center of the bottom (I think it said about a 1 mile hike), it was worth the hike! When we got back to the top, we visited Volcano House and the visitor center (in the future I would skip those two), but our final stop at the steam vents was very worth it, there are even steam vents in the parking lot if you don't want to walk, but we walked around for some better views.
11:30am Auntie Pon's Thai Food truck was supposed to open, but it didn't, people love this place, but we were quite annoyed that they weren't open by 11:50, so we left, skip this truck.
1-2 played at Punalu'u Black Sand beach, this was a beautiful stop and very worth it!
2-3 ate at the Southernmost restaurant in the US (Hana Hou). By now we were starving so would have settled for any food we found. Food is very hard to come by, and this place hit the spot. Don't go out of your way for it, but it was good, and we couldn't find food anywhere, try to make a plan for food, so much was closed on Mondays.
3-4 drove back to Hilo
4-5 since we had some time, we visited Rainbow Falls, you can see it from the parking lot, so it can be a quick stop. We spent some extra time since my son climbed the big banyan trees there, and they were impressive to look at.
5:30 arrived back at Hilo airport, for our 7pm flight
I wouldn't change anything, it was a great day. However, next time I might pack a lunch since it is really hard to find any food places open on a monday.
Hope this helps if anyone else tries it! I'm very glad we didn't book a tour, it gave us time to explore the way we wanted, especially the volcano hikes, and the specific black sand beach we wanted to go to (Punalu'u was very beautiful).