What is the religious ruling regarding a man who divorced his wife with a contingent divorce based on visiting his mother, and then after reconciliation and taking his wife back, he demanded she be considered a widow, desiring to resume his relationship with his mother?

Your question is unclear. If the intention is to ask about a man who conditioned his wife's divorce on her not visiting his mother, then the majority opinion is that if she does not visit his mother within the time he intended with his oath, her divorce occurs. This is the fatwa we follow. Some scholars, like Ibn Taymiyyah, may Allah have mercy on him, held that if the husband did not intend for the divorce to occur by his oath, then his divorce does not occur if he breaks his oath; however, he is obligated to offer an expiation for an oath. If the condition was phrased as: "Consider yourself a widow," this is not an explicit declaration of conditioning divorce. Therefore, if the husband did not intend for divorce to occur by it, then no divorce occurs, and he is not obligated to offer an expiation for an oath if he breaks it.