You would prove that there was a pre-existing marriage (to your mother-in-law). The family of the second "wife" can then try to *disprove* that he was still married to the first when he married by the second, such as presenting evidence of a divorce (if there had been one). You don't need to prove a negative (that a divorce was not filed); you just need to prove the positive (he was already married when he "married" the second woman), since once a person is married, he stays married unless and until there is a divorce.