At 2, my daughter enjoyed various things at Epcot, AK, and DHS.
Epcot: She loved meeting characters so we met quite a few around the world showcase and Character Spot. She also enjoyed Nemo and Friends and Turtle Talk. She really enjoyed the Boat ride in Mexico. She really enjoyed Splashing in the Fountain in Future World. Surprisingly, she did like Living with the Land. She didn't care for Spaceship Earth. It was a bit long for her at that age. She wasn't afraid of it just not really her thing.
DHS: She LOVED the Disney Jr. Show, Beauty and the Beast Show, and the Ariel Show. She enjoyed the Honey, I Shrunk the Kids Playground. She did not care for the Great Movie Ride (while she liked the Wizard of Oz section- it was just too long for her). She really liked meeting the Disney Jr. characters.
AK: She loved the Boneyard play area especially the sandbox. She liked the Safari and the petting zoo at Affection Section. She really enjoyed the Lion King. She got to dance in the show, which she loved. She liked the Nemo Show. I was afraid this show would be too long for her. Since she loves the movie, it actually held her attention. We didn't try It is Tough to Be a Bug.
For us, we found enough stuff to do to fill an entire day at AK, a day at DHS, and two days at Epcot. However, we did also have sit-down meals at all parks and we tend to move slowly.