Is marriage and divorce without a guardian invalid, and can the spouses return to each other without the need for a "muhallil"?

Scholars differ on the ruling concerning marriage without a guardian (wali), and the fatwa issued (mufta bihi) is that it is invalid. They also differ on the ruling concerning divorce in a marriage whose validity is disputed, and the preponderant opinion (rajih) is that it takes effect. Accordingly, a man cannot marry the woman again unless she marries another husband and he consummates the marriage with her, and then he divorces her, as stated in verse 230 of Surah Al-Baqarah. However, if there is a need to adopt the other opinion, which holds that divorce does not take effect in a disputed marriage, in order to alleviate hardship, then there is no harm in doing so, provided that it is not merely a pursuit of legal concessions.