Your kids will have an absolute blast. Kids club opens up at 9 AM I think, most families drop off kids after breakfast, and many start picking up around 12-1 for lunch. I believe 4 year olds are the limit for pure "drop off" and your 1 year old could be there with one of you, or you can also hire babysitters hourly as well.

-I was on points+cash upgrade, but did not incur any additional surcharge for my one kid. Two I'm not sure, but I think your ages should be ok. One can probably use a crib and the other, the side "sofa" which got made into the kids bed for us.
-If there was supposed to be a kids charge for breakfast, I never saw one. Certainly your 1 year old wouldn't incur any charge, and even if your 4 year old did, it would probably be nominal. I was never explicitly told they would be free though, so YMMV. I am also a Platinum currently, so not sure if that played into the equation.
-Regarding kids meals, they have a kids menu that is accessible at every single restaurant. I really appreciated this, as my kid could order the same meal regardless of which restaurant you're at. For example we were set to do a tasting menu at Iwau, and he would have been able to choose from the same kids menu at Locanda. That being said there were plenty of dishes at the restaurants that my 6 yo also shared with us. My kid took ALL of the shrimp from my seafood extravaganza at Beach Shack for example!

Currently the kids menu is $15++ for the entree and includes juice
-Vegan rice paper roll and tamari
-Ham and Cheese + fries
-Mac and Cheese with Ham
-Grilled chicken, veggies, rice
-Baked Salmon
-Steamed Fish
-Mini Cheeseburger
-Penne Tomato Pasta

Let me know if you have any other questions.