Is it permissible for a son to perform Hajj on behalf of his deceased mother, or to carry out an ongoing charity for her, if she followed a school of thought that contradicts that of Ahl al-Sunnah wal-Jama'ah?

The reward of charity and Hajj reaches the deceased without any scholarly disagreement, even if his mother was an innovator, as long as she was among the people of Islam. As for declaring some innovative sects as disbelievers, Sheikh al-Islam Ibn Taymiyyah preponderated that their statements of disbelief do not necessitate declaring a specific individual a disbeliever until proof is established against him, because the default assumption for them is Islam. This is why your husband was given a fatwa (definition) permitting him to dedicate the reward of acts of worship to his mother.