Blizzard Beach and Typhoon Lagoon both have special kids areas - my dd (4 1/2) prefered the BB one, but for a 2 year old it could go either way.
At BB they have mini versions of proper slides, so they can do a real tube ride, actually there are a couple of slides (3 I think), there is also a nice shallow pool area, also no sand, which for me is a bonus, as the sand seems to get everywhere!
At the very top of this area is a really small play area for the tiniest babys, so everyone would be accomodated for in some way. We also say Goofy in the kids area which was fun!
at Typhoon Lagoon, the kids area has a shallow stream they can paddle in, and quite a few things with water that can be squirted, my dd really didn't like that since it kept getting her face wet, and she doesn't like that, so we didn't spend as long here.
We have never taken dd to Disney Quest, I think she's a few years away from appreciating it.
Bev