Is opposing a mother’s marriage to a married man who is a provider considered a violation of Sharia, taking into account society’s negative view of such a marriage and the potential for it to result in the divorce of the other wife?

It is not permissible to prevent a mother from marrying a competent man on the pretext that he is married and has children, for that is not a defect that compromises competence. The fact that the marriage might lead to the divorce of his first wife is not an impediment, unless the mother stipulates that he divorce his first wife, for this is not permissible due to the prohibition of the Prophet (peace and blessings of Allah be upon him) against it. Dutifulness to one's mother is among the most obligatory duties, and disobeying her is among the greatest major sins.