Is swearing an oath that the father of the children "works and is employed" in court considered a lie, knowing that he does not work, and what is its expiation?

The great mistake and grave sin you committed was swearing an oath upon the Qur’an. You should have clarified the whole truth to the judge so that he could issue his ruling on a sound basis. Now, you must immediately repent sincerely to Allah, and it is safer to offer an expiation for your oath.