I hardly understand the comparison to drink driving. Breaking the law doesn’t by default make one a danger to their children.
Nor should punishment for breaking any law be to separate a family. Children shouldn’t suffer unnecessarily at the hands of the law, regardless of the choices their parents make.
If actually convicted in court for illegal immigration and are to be sent to jail, than there is no choice but to separate the child from the parent, but until that point, they aren’t guilty and neither they, nor their children should suffer