codice:
public class JDialog_1 extends JDialog implements ActionListener {
  
  

  public void faiQualcosaConVector (Vector v) {
  /*
  */
  }

  public void actionPerformed(ActionEvent ae) {
    JDialog_2 jd2 = new JDialog_2(this, eventuali altri parametri);
    jd2.setVisible(true);
    ...
  }
}
codice:
public class JDialog_2 extends JDialog implements ActionListener {

  private JDialog_1 jd1;
  Vector v; //lo creerai da qualche parte

  public JDialog_2 (JDialog_1 jd1, ...) {
  /*
    this.jd1 = jd1;
  */
  }

  public void actionPerformed (ActionEvent ae) {
    jd1.faiQualcosaConVec(v);
    jd2.dispose();
  }
}