Is a marriage that took place without the guardian's consent, and in which divorce occurred three times at different intervals, valid and binding?

You divorced your wife with three pronouncements, so she has become irrevocably separated from you (baynunah kubra). It is not permissible for you to return to her until she marries another husband in a desired marriage, and he consummates the marriage with her, then divorces her or dies, and her waiting period (iddah) expires. Even if the first marriage was without a guardian (wali), this return is not permissible; because a nikah ash-shubah (marriage of doubt/semblance) entails consequences such as offspring. How then can it be permissible for someone who believed in the validity of the marriage to go back and base a ruling that suits his desire on its invalidity? And after the triple divorce, no one is allowed to scrutinize the guardianship to use the guardian's فسق (immorality/disobedience) as a pretext for the divorce not taking place, for the majority of jurists validate the guardianship of the immoral person and uphold the divorce in such a marriage and other فاسدة (corrupt) marriages.