We just took our DD for the first time last october...just like you we have gone many many times as a couple and were really excited about having our little girl see WDW! She loved it! Here are the things she loved:
AK: She loved Dinoland...there's a triceratops ride (thinks Dumbo), carnival games & the Boneyard (big playground). Warning: the Boneyard is big and can be difficult for the little ones to get around in...rope net ladders, long slides...there's only one way in and out, but we did a tag-team approach with one person on the ground at all times so that when she came off a slide she wasn't alone. She also loved the tigers in Asia...
MGM: I know you said shows probably wouldn't work & we thought the same thing, but Disney shows are sooo different. I highly recommend Little Mermaid...my DD loved the effects! Also at MGM, the Honey I Shrunk the Kids playground. Much more toddler-friendly than Boneyard, but two adluts still necessary in my opinion.
EPCOT: The Living Seas was closed when we were there, but I know she would have loved it. She loved the Land, Imagination, and Soarin' (she'd really tall, though &^ I'm not sure a 2yo would be able to ride). I think there is a play area at Mission Space, but we didn't make it over there so I'm not positive.
DTD: The
Lego store has a really cool play area outside that she enjoyed for hours!
Basically any ride was cool with her...for that matter, any ride, character, statue, balloon vendor, duck, shop...you name it she loved it! Don't forget to make ADR for character meals...we did several & I'd be happy to advise there, too, if you want.
I hope this helped. Don't forget Toontown at MK...there is so much cool stuff there that DH and I never did as a couple...and some very special opportunities to meet the characters.
Have a great trip & PM me if you have any more questions!