Agree with everything Meals has put but also to add if you go to the Dolphinarium it is in Creekside Park and if you go there that could be a whole day out. Included in the park is Childrens City (mini science museum) which my 2yr old loves; cable cars which are great for whole family and gives a nice view over the creek area and then the park itself and all that entails. It is one of our favourite locations as we can do something different each time.
We also like Mamzar Beach (but any beach is good), amazing how much time DD can spend just moving sand and water around lol. Playnation / Magic Planet in the malls are also good to let them run around. Aquaplay at MCC is good and at 2 she should just be about okay if you go with her and help with some of the levers/buttons etc.
We've also done the Aquarium, Burj Khalifa, Bus Tour etc with our DD and she was pretty interested in most things as long as there was something good to look at or she had a bit of run around time.
Aquarium and discovery centre (Dubai Mall).
Parks - Safa/ Barsha etc
Dolphinarium
Play areas inside shopping centres.
Beach (bit cold to swim, but lovely to play in the sand on the beach).
Kidzania (prob a little too young though).
There's heaps to do with LO's here! :)
My sister is panicking about what she will be able to do here with my 2 yr old neice (she's coming for a weeks holiday in April) and as i don't have kids, i'm really not able to advise....any recommendations would be greatly appreciated...cheers