Actually, that's not entirely true. The judge did address the wife:
Diaz-Salazar in fact was separated from a wife and two children whom he had left in Mexico in 1974. Thus the woman with whom he lived in Chicago and by whom he had two children born here was not his wife, although he seems to have considered her so.
You're right, they did say that. At the same time, the sentence you quote apparently refers to the period of time when the children were born. By the time this case got underway, he had divorced his Mexican wife and married the woman in Chicago. So the "relevant facts" sentence, which is in the present tense, is accurate in simply saying "the petitioner has a wife."
I also note that, despite the fact that the mother was not his legal wife when his children were born, the judge still calls the children "natural-born." In other words, in this case at least, the offspring of an illegal immigrant by a woman he's not even married to have been labeled "natural born."