Will a divorce occur if the wife does not go to spend Ramadan with her husband's family after the husband swore to that effect? And what is the ruling on his oath if the wife goes, and the husband's parents tell her to return to her family's home due to her exams?

The relied-upon fatwa with us is that whoever made his wife's divorce conditional upon a condition cannot retract it. If the condition is met, the divorce occurs, whether the husband intended to enact it, or intended a threat, emphasis, or prevention. This is the opinion of most scholars.

Shaykh al-Islam Ibn Taymiyyah is of the view that if someone intended to enact divorce, he may retract it. If he did not intend to enact it, but rather intended a threat, emphasis, or prevention, then divorce does not occur, but he is obliged to offer an expiation for an oath (kaffarat yamin).

Accordingly, the husband breaks his oath and his wife is divorced if she does not go and spend Ramadan with his parents, unless he intended by his oath merely for her to go to appease them and they were pleased with her return.

Since her divorce has occurred, and it does not complete three divorces, her husband may take her back during her waiting period ('iddah).

As for the view of Ibn Taymiyyah: if the husband intended the divorce to occur when the condition was met, he may retract it, and his divorce does not occur, but he must offer an expiation for an oath. If he intended a threat and encouragement, and did not intend to enact divorce, then if she does not go to his parents' house, she is not divorced, but he must offer an expiation for an oath. It is recommended to consult the Sharia courts or directly ask people of knowledge in such cases.