I would definitely recommend a split stay, planning your east coast (Windward) activities around your Waikiki stay. Lots of very good hotels in the Waikiki area for 50% of the Aulani/Turtle Bay rates. And if you’re using the days to see the sites, it’s really kind of a waste to pay the premium.
You’ll definitely get some polarized opinions on this topic. From my perspective (grew up on Oahu, visit family every year since the 90’s), there’s so much to see and do from the south eastern portion of the island, that having to drive from the Ko’Olina or North Shore areas really misses out on one huge element of a great Hawaii Vacation - “Island Time”. Slowing down, taking it easy, and having time to do whatever, whenever.
Soooooo many great restaurants and experiences in the Waikiki area. Instead of rushing to do the Diamond Head hike, with 1.5 hours of driving to and from the resort, stay some place 10 min away, and have the extra hour to hit the farmers market across the street for a cold drink and local food. Or make an extra stop for shave ice, and people watching. Or go to a truly great local food restaurant (Helena’, MW Restaurant, etc) that you wouldn’t go to if you had to drive an hour to get to. Waikiki does have its downsides, but lots of positives too.
Haunauma Bay is much easier if you’re on the windward side. I don’t know if I’d recommend the Dole plantation. If your kids were younger, definitely fun, but at this age, really only the maze would be much fun. I’d suggest planning a hike to a waterfall or a lighthouse. And definitely plan for a good shave ice shop (Uncle Clay’s, KokoNuts, or Waiola), and malasadas at Leonard’s on Kapahulu.