I would lean Kidani. 1 and 2BR have an extra bathroom. The animals can make for a little extra in-room entertainment. Kidani's pool area is a bit better for young ones.
OKW's biggest drawback is most buildings have no elevator, so you may be lugging 3 kids worth of supplies and/or sleeping kids up and down to your 3rd floor room.
I'm an OKW lover and we stay there most often, but, in your situation, I, too, would recommend Kidani. You'll appreciate the extra bathroom and the animals. Dining is better there. You can get room service. And the pools are more kid-friendly.
DH and I have stayed at kidani and are going back with the kids for our next trip. We have never stayed at jambo so I can't Compare but I have heard the pool at kidani is great!
i guess I am the minority here but I say OKW. I have stayed at both and I love it at OKW. It is my fav resort. While you may loose a bathroom the room is so big. I have stayed on the 3rd floor at OKW with two stroller age kids and while not ideal it wasn't a big deal. I like that at okw when you leave your room you are outs de. I felt like I was at a hotel at Kidani...just mho. I also like the layer back nature at OKW. I did't like that Kidani didn't has a QS if we wanted to grab something. We usually make our own meals but sometimes we wanted to grab something.
We really enjoy the boat to DTD front OKW and we enjoy visiting SSR for lunch. I am sure you will be happy at either. We did enjoy the animals at kidani. I am from canada and I like florida so I like feel like I am in florida when I go. Have a great trip
Another vote for Kidani. The extra bathroom would be great with a big party. The splash area by the pool is great for little ones. When my kids were young they were amazed by the animals there. They used to sit on the rocking chairs watching the animals with their toy binoculars. It was adorable.