Hm, well, maybe KHII can answer this, though I wouldn't think she's Ansem's daughter.

Anyway, Kairi's one of the Princesses of Heart. She was born on Hollow Bastion, but didn't remember at first. (Or she had dreams of it..or something like that.) I don't really think they mention her parents...but I'm not really an expert on KH, so if anyone knows, I'd sure like to.