Is a married woman obligated to stop her studies and not leave the house based on her husband's request, under the pretext that intermingling (with the opposite sex) is forbidden?

The fiancée is not legally obligated to obey her fiancé before the marriage contract; obedience is due only to the husband. However, it is obligatory to obey whoever enjoins a duty or forbids a prohibited act. So, if mixing with non-mahram (definition) men is without legitimate Islamic controls, then it is forbidden and must be abandoned. The fiancé has the right to prevent his fiancée from forbidden mixing. As for preventing her from going out for study or work absolutely, while adhering to Islamic controls, it is not his right, and she is not obliged to obey him in this matter. She may obey him if she sees a benefit for herself in doing so. A woman's decision to stay at home is better for her if she is financially provided for.