Is it obligatory for a husband to endure his wife's repeated insults because of his dutifulness to his elderly mother, or should he resort to threatening divorce?

Kindness to parents is one of the most obligatory duties, especially in their old age. You must be kind to your mother, whether your wife approves or disapproves, for in it there is blessing and obedience to the Lord. As for your wife, it was more fitting for her to assist you in being kind to your mother, rather than to complain. We advise you to remind her of Allah first, then to forsake her in bed, and to strike her a non-injurious blow. If she does not return [to righteousness], then threaten her with divorce. If she persists and there is no corruption in your religion or worldly life by remaining with her, then patience with her is more befitting.