Using 'hound out' implies negative behavior and emotional distress for the person affected. She was hounded out of the committee for her differing opinions.
Pro Tip 2/3
Persistence
'Hound out' conveys a sense of relentless pressure, often over a prolonged period. Journalists hounded the politician out of office with continual scrutiny.
Pro Tip 3/3
Forceful Exit
The phrase often suggests that the person leaves against their will as a result of the harassment. After months of being hounded, he was finally hounded out of the neighborhood.