Is it permissible for a mother to use her رضا (pleasure/approval) or عدم رضاها (displeasure/disapproval) with her son as a means to make him return from studying in lands of disbelief (bilād al-kufr), and does the mother incur sin if her husband becomes angry with her for opposing their son's travel abroad for study?

The basic principle is that a Muslim's residence in disbelieving lands is prohibited due to the danger it poses to their faith and morals, unless the Muslim is safe from temptation and able to openly practice the rituals of their religion. In such a case, it is permissible for them to reside there to achieve a religious or worldly benefit.

The warning mentioned in the Hadith (definition): "I am innocent of every Muslim who resides among the polytheists," is interpreted as referring to those who are not safe regarding their faith.

Therefore, if your son is safe from temptation and able to openly practice the rituals of his religion in that country, there is no harm in his residing there for study, and you are not obligated to forbid him. However, if his residence exposes him to temptation in his religion, then his residence is forbidden, and you must forbid him from it and inform him of your disapproval until he returns. Your husband's anger about this should not concern you.