I explained how Kairi got there, unfortunatly we can only speculate as to why, personally I think it was as the world was bing swallowed by Heartless someone sent her away, maybe it was DiZ/Ansem in an attempt to redeem himself or her grandmother.

Sora wants to leave Destiny Islands with Riku and Kairi because they want to see more of the world. Then the Heartless attack and he gets swallowed up and sent to Traverse Town.