Why could Ishmael and Isaac have no interrelationship?
They could have no interrelationship because Ishmael represented the law, legalism, and the flesh, while Isaac represented grace, freedom, and the spiritual promise. Scripture says the son of the bondwoman shall not be heir with the son of the free woman, so the bondwoman and her son were cast out.
Les explains that Galatians uses Isaac and Ishmael as an analogy. Ishmael was of the flesh, earthly, not of the spiritual seed, and not of the promises as Isaac was. Hagar and Ishmael stood for the law and for that which is of the flesh. In Galatians 4:30, Scripture says, "Cast out the bondwoman and her son," for the son of the bondwoman shall not be heir with the son of the free woman. Therefore, Ishmael and Isaac could have no consort or interrelationship, because Ishmael stood for the law and legalism, while Isaac stood for grace and freedom.
Nevertheless what saith the scripture? Cast out the bondwoman and her son: for the son of the bondwoman shall not be heir with the son of the freewoman.