Or consider this, you who think that divorce nullifies a marriage, is it not written that "Anyone who divorces his wife and marries another woman commits adultery against her. And if she divorces her husband and marries another man, she commits adultery." Mark 10:11,12 Now if divorce nullifies a marriage then how could it be that adultery is committed if a new marriage takes place? It can only be if the initial marriage was not nullified. In fact even after God declared Himself divorced in Jeremiah 3:8 He nonetheless says a few verses later, "I am your husband." Jer 3:14 The divorced are both single and married. Notice 1Corinthians 7:10,11 The Lord declares, "A wife must not separate from her husband. But if she does, she must remain unmarried or else be reconciled to her husband." Here an unmarried women (unmarried through divorce) is spoken of as having a husband, and in fact as obligated to stay single or else be reconciled to that husband.
So when we read that God divorced we must realize what God's attitude towards divorce is. He does not give up on Israel. In fact he reconciles with his wife. In practice God's divorce is more like what many think of as a separation. And in fact such separations are not uncalled for even in the Christian community. But such is for the purpose of discipline through public shame, as Israel was also discipline by God despite being his wife.