I haven't been there in a few years, but I doubt much has changed in terms of shade - there wasn't much of it when I was there. I think they try to limit the amount of shade foliage both to reduce the amount of stuff that gets in the water and to drive up demand for cabanas. I wish they had more of the long awnings like most parts used to, but don't expect much. If there are any awnings to hang out at, they'll be down by the big kid's play fort.
Don't expect to be able to dump all your stuff in one place and leave it though, I have a feeling they prevent people from doing that in order to sell more lockers/cabanas, and to prevent the shaded areas from being taken over all day. If one of you stays with the baby in the shade, it probably won't be an issue.
Hope you have fun. Let us know how it is, we don't get many reports from White Water.