I'll try to help you as I've been to all 3 hotels you are considering. I also liked all 3 and would return.
First off, if you have kids, you might want to pare down your island-hopping. No matter how early or how late you make your flight, island hopping does cut into your day, and with kids it's even worse logistically.
If this is your first-and quite possibly your only trip to Hawaii in your lifetime- then yes, do all 3 islands. All 3 are SO different and unique that it's a shame that some people can only visit one or two.
I find Kauai to be the island best suited for adventurous people....lots of hiking, nature-based activities, beautiful scenery, no nightlife....so keep that in mind if you do need to cut an island out. Also, if the Pearl Harbor Arizona Memorial is a must-see for you, then by all means keep Oahu in your plans. The Big Island almost defies description and has to be seen; it's our favorite island (besides Molokai) and I would definitely suggest you go there as well.
The beach at Waikoloa was, in my opinion, very nice. Lots of water activities there...huge green sea turtles and fish swimming alongside you....took a great catamaran cruise/whale watch from there (the beach is called A' Bay, short for Anaehoomalu Bay)..they also had kayaks, water bikes...I liked it. You can walk to the left for more seclusion. Nice for snorkeling. Although people may indicate that this resort is not 'on the beach', there is a short, interesting walk to the beach that would only be a chore for the handicapped or really lazy.
The JW Ihilani beach area consists of four man made lagoons and it is not an 'ocean' feel, per se. You can access the ocean from the JW but there really is just a rocky edge there, no accessible public beach, so the lagoons are basically it for sunbathing.
Kauai Beach was decent; not huge, and as I recall, a bit too cloudy to snorkel....plus, there was a strong undertow and I wouldn't recommend venturing too far offshore there. Nice views of the incoming cruise ships and the helicopters that tour the island. Good for getting your feet wet and sunbathing.
The Marriott Waikoloa has very limited food choices on site; literally one restaurant and a bar-type menu. The food was good; just not many choices. The Kings Shops directly across the street have some nice restaurants; we went to Roy's and had a great dinner. I believe Merriman's also has a location there.
Kauai Marriott had an on site Dukes Restaurant which we enjoyed. There were several other nice restaurants on the property and they had a sushi restaurant that looked very nice, if that interests you.
The JW had some great restaurants, among them, Azul....which I just recommended to another FTer yesterday....great food and a very extensive wine list. Very personalized service.
My thought is, if you can throw on a few more days to your trip, it might help. Two nights on the Big Island is not a lot, especially if you plan to do the volcano. There's a reason it's called the BIG Island
I hope that helps some. Feel free to ask more questions and I'll be happy to help. You will have a fantastic time no matter what you do!