If the husband provides a separate home, is it permissible to not interact with his mother and to not allow her into the house, given that she causes problems and ruins relationships?

If the husband's mother is ill-mannered and unjust, it is permissible to avoid her in order to avert harm, even if a graceful disengagement is better than harmful interaction, as mentioned by Al-Hafiz Abu Omar ibn Abd al-Barr. However, if one is safe from harm, it is better not to avoid her, because pardoning an offender is among the best deeds, and responding to evil with good brings affection and protects against the evil of Satan.