You seem to be making assumptions. How do we know the wife and kids did not come first, he came to visit on a B-2 visa, then somehow got a work permit. I don't have any doubt he is in the US illegally since his work permit expired in March but I have not seen anything that says the entire family was in the same situation. Can you post a link to something that details the visa status of the wife and kids (something besides politician statements)?

Judge Blocks Deportation of Family of Suspect in Colorado Attack
Lawyers for the wife and children of the man charged with attacking an event supporting hostages in Gaza filed a lawsuit on Wednesday seeking their release.
The suit says that Ms. El Gamal and her children entered the United States on tourist visas in 2022.