And from what I understand, the Clintons went to great lengths to raise her as well as possible...and again, from what I understand, it seems to have worked.
And as for the effects of her father's philandering...she's not the first kid whose father was caught getting blown at the office. She won't be the last, either. Of all her father's actions in the office, odds are it's his actual job that had the most impact on her.
I still think, though, that she looks like the "desperate intern" sort, however.