Do you know where you will be staying? Some of the bigger hotels or condo complexes have children's activities and even play areas, but, of course, it's more pricey to stay in places with a lot of amenities. Below is a quote from a review on Trip Advisor. I got this by googling "Kauai children," which I suggest you do.
"My family has been going to Kauai since our children were first born. They are now 14 and 12. When they were small they were thrilled with the beaches and the incredible walks in warm weather or pouring rain. We have gone for three weeks at a time and found a new beach every day to explore. They have done snorkelling and hiking and watched wind sailing. They have made leis and been thrilled at Smith's luau. As they got older, they did shopping, and beaches, pools and hot tubs in the rain, wave bashing (standing in the knee high water and letting the big waves wash over you.)They have investigated huge caves and walked through sugar cane fields (maybe even took a little piece of cane to go.) They take flashlights at night to watch the huge toads you can find. They try to catch the small hermit crabs on the beaches (never can) and try to find the geckos asleep in hibiscus. Now they are older and have gotten to kyak up the river, walk through the jungle, swing on ropes into pools of water and visit the bottoms of waterfalls and sit underneath them. They have done Captain Andy's day trips and seen turtles and dolphins and whales and flying fish. They have sat on the trampoline tarp while the waves wash up on them and snorkled in the deeper parts of the ocean. There are wonderful parks for kids and really safe ocean places to play (Lydgate)and every one you seem to meet is friendly when you are yourself. Believe Me, your kids will love Kauai. "
I'm not sure how the weather is in November, but generally the south end of Kauai has more sunny weather. The north end (Princeville, Hanalei to Ke'e Beach) tends to be rainier. When you venture out on day trips, check the weather report in advance, if that matters to you.
You also could google "Kaui webcams" this month to see some of the resorts and what the weather might be like in different areas of the island.
Planning is half the fun!
