That's right. He isn't allowed back here. Also the reason he was deported is because he wasn't an american citizen, just a permanent resident. But he can never come back. If he had become an american citizen and carried dual citizenship, things would have been different. But even then, certain people are not permitted to become a citizen, if they are not seen as an upstanding person or they have a criminal record, etc.

If your kids are born here, they are automatically american citizens, but in his case, where he was not a citizen, that automatically gives his children dual citizenship with Italy, which they will keep unless they would ever renounce their italian citizenship.