I can much more easily enjoy 15 days in Oahu vs Maui (or most other island locations in the world, really) --- but to each their own. Sure there is lots of tourists, but the 'crush of tourists' in Waikiki is near where near the crush one experiences trying to visit the highlights in Paris, Rome, Venice, etc! Several years ago I lived in Waikiki for 11 months straight just a block from the HR, and I never really got tired of it, -- heck, I am thinking about looking at doing a sabbatical at UH-Manoa the year after next and stay for ~8 months.

As for Island hopping -- I agree with the sentiment that you shouldn't underestimate the pain of spending a few hours between ground transportation and through airports while vacationing in Hawaii. I recommend the Big Island to at least visit Volcano national park, some black sand beaches, rainforest hikes with waterfalls, and I like driving up Mauna Kea for their star-gazing program. Hilo is an authentic quiet town with plenty of stock of affordable (though aging) hotels that makes a good launching pad for these non-resort scene adventures (compared to the chain restaurant filled, resort property lined Kailua kona side). For me, the highlights of the Big Island provides the most significant add-on to the Hawaii beach scene that you get plenty of in Oahu or Maui. Just be sure to pack a jacket as it is quite chilly at higher elevations, and there isn't any Hyatt on the Big Island (though, I think there is some overprice condos in the WOH program now? I looked a year ago and the availability was near nothing and the price was too high).

I'm going next month -- 2 weeks in Oahu (first part at the HC, second part at HR Waikiki) with a three day break on the big island right in the middle. Plan on using the bus to get around in Oahu (or occasional uber/taxi), but definitely have to rent a car on the big island -- rental rates are decent there too. Not sure about how to handle bag situation -- but leaning towards doing my best to get the family to pack light.