When DD was 2 we took her first trip. We were at EPCOT a full day from open to close and wished we had 2 days there. It was by far her favorite park other than MK. DD could have ridden the boat ride in Mexico around in circles all day and had great day. She also loved the Living with the Land ride (something about those greenhouses that every preschool I know who has been on it has loved), the Nemo ride, Turtle Talk with Crush, Journey into Imagination, Spaceship Earth, the Aquariums after the Nemo ride, and the play areas after some of the rides (mission space has a fun play area- where someone can take them while others ride). She loved meeting the tons of characters, watching the entertainment like the juggler, acrobats, bands, drummers. She liked exploring the countries, watching the trains in Germany, looking at the fish in the pond in Japan, banging the drums at the outpost, and the hedge maze in UK. She loved the Kidcot stations where she could color and get stamps from each country. If you are looking for an ADR, Biergarten is a lot of fun for that age with the German band and a dance floor where they can go out and dance. EPCOT is a really good park for that age because there are plenty of areas and play areas for them to walk around and explore, if you just take the time to smell the roses! All the grandparents loved EPCOT too.
As far as the other parks, DD did not like AK at age 2. It was not enough of a Princess presence for her (basically there is none), and she pretty much equated it to the zoo at home. I really enjoy AK, but she was begging to go back to MK or EPCOT. As far as DHS, she has always loved shows and would sit through them from an early age. As a result, she liked DHS, which is show heavy. If your 2 year old won't sit through shows, you might run out of things to do at that park after a while. Also, if your DD is sensitive at all to loud noise and villain stuff, be a little wary about Fantasmic. You might try sitting towards the back if you are going to do it, where it is not as loud and where you can make an exit if need be. Fantasmic really scared DD when she was 2. I had seen it before and watched it online again before taking her and thought it would be fine for her, but it is quite a bit more intense in person than online, especially if you are sitting closer to the front.
Have a great trip! DD was 2 months short of age 3, when she had that first trip, and I think it was my favorite WDW trip ever. Everything was new, wonderful and magical to her.
