We've been twice, and while the Big Island was our second trip, I'd recommend it for a first timer.
The Big Island is where Volcanoes National Park is, and it's home to Mauna Loa and Mauna Kea.
The island has a much more laid back, rural feel and is easily drivable. You can hit Volcanoes National Park on your own and do a variety of self-guided activities or book guided hikes. We really wanted to visit the Thurston lava tubes when we were there but couldn't because there was an active eruption.
There is a sunset tour to the Mauna Kea summit to see the sunset. Your youngest may be too young (only a couple of companies do this tour, and there was an age limit when we booked it). But you can go to the visitors center and view the sunset there.
The Big Island is also one of only two places in the world where you can snorkel with Manta Rays. I highly recommend this.
The beaches are a bit rougher, but you said this is your lowest priority. I don't know what your budget is, but the Fairmont Orchid has a fantastic beach with a protected lagoon where you can snorkel, SUP, etc. It's really amazing.
There are a lot of great waterfalls on the Big Island (easy to drive to) and there are a couple of botanical parks that fit your "jungle" interest.
Check out a website called Love Big Island for more info about sightseeing. Big Island Guide is another good website.
Logistically, you will prob want to fly in/out of Kona (KOA). Hilo is closer to the Volcanoes National Park, but I don't think you will want to spend your whole trip staying in that area. I would either stay in Kona and drive or do a short split stay with most of your nights in Kona.
There are some pretty neat accommodations near Volcanoes National Park that would give you a "sleeping in the jungle vibe". There is Volcano Inn, Volcano Village Lodge, Volcano House (actually has views of the crater), and others.
In Kona, there is a good mix of chain hotels and Airbnbs.
The Big Island was a one-island trip for us. There is plenty to do to keep you busy for a week. Our first visit, we did Oahu, Maui, and Kauai all in one trip. While I enjoyed all of the islands we've visited, The Big Island is my favorite.