My dd loves Finding Nemo, too. (The first few minutes are scary, though.)
Dd is almost 4 and also very sensitive to movies; she is afraid of scary/ominous music, scary/ominous lighting, people yelling/arguing, etc. I honestly don't think she could handle some of the scenes in Mary Poppins, such as the scene at the bank.
We have Netflix, so can stream all kinds of material. She loves to watch episodes of Dora the Explorer.
A movie we found that she adores is The Ballet Shoes. She also liked Fly Away Home, but there is a kind of sinister guy in there trying to thwart their efforts.