Is it obligatory to visit the mother after she slandered her daughter's reputation and tried to destroy her home, knowing that she recently underwent an operation?

If the mother has done what you mentioned, she is gravely mistaken, for harming a Muslim and defaming their reputation is forbidden, so how much more so when it concerns kin, whose ties must be maintained. You must search for the reason for her anger and strive to mend the relationship with her through supplication and the mediation of people of goodwill. Abandoning the mother is not permissible, even if she is a disbeliever; rather, one must accompany her with kindness. Some scholars permitted abandoning them for a legitimate religious benefit, but mostly there is no benefit in that. It is better to maintain ties with her and visit her to soften her heart and win her affection, and repelling evil with good may turn enmity into friendship.