Instead of going through the mess she did as a kid, Nami was raised one of the following:
Goku and his family.
Ranma and his father.
Luffy's grandfather, along with Luffy and Ace.
How does she turn out? Even after the trouble with Arlong part of me likes to think her obsession with money is due to the trauma seeing her mother being killed over money, having to get try to get enough money try to buy back her towns freedom, with her family being poor from the start just adding to that.