This depends upon which word you wish to emphasize.
Ignominious - (adjective) deserving or causing public disgrace or shame
Ignominy - (noun) shameful or dishonorable quality or conduct or an instance of this.
Infamous - (adjective) well known for some bad quality or deed
Infamy - (noun) an infamous act or circumstance.
If you pay careful attention, these are very close in meaning with subtle yet powerful differences interpreted when I encounter them in use.
If you wish to emphasize "bad" or "shameful" then forms of
Ignominious are the better choice, to my ear.
If you wish to emphasize "legacy" or "perception" then forms of
Infamous ring clearer.
So, to use your example sentences:
"Hitler's ignominy still haunts modern Germany"
"His ignominy caused them to expatriate him"
Each of these places emphasis on the deserving of shame without necessarily placing concern on the expanse of his notoriety.
"Hitler's infamy still haunts modern Germany"
"His infamy caused them to expatriate him"
Each of these places emphasis on the public opinion of perceived acts.
One can be infamous for things not done, but one cannot be "ignominious" without being deserving of the label. Ignominious is the stronger term here, because it directly asserts causation between acts and the label where infamy merely connotes a correlation between perceived acts and the label.