Does a divorce take place for the wife if the husband swore that if his daughter registered for a second semester at the university, his wife would be divorced, and the intention behind this was to demonstrate seriousness to his daughter so that she would succeed in all first-semester courses, and then he wished to retract that after her failure in all courses?

If your daughter registered at the university in the second semester, a divorce has occurred according to the view of most scholars, which is the relied-upon opinion for fatwas. Sheikh al-Islam Ibn Taymiyyah holds that an oath of divorce not intended to effect divorce but rather for threat or emphasis, takes the ruling of an oath by Allah, thus requiring an expiation for an oath and not resulting in divorce. You are not permitted to retract this oath. If the divorce occurred and it was not the third divorce, you may take back your wife during her iddah (waiting period). The permissible oath is by Allah Almighty, whereas an oath of divorce is among the oaths of the dissolute and should be avoided.