Is it permissible for my wife to travel with me after I told her: "It is forbidden for you if you go on the trip with me," and then I changed my mind?

The ruling on swearing by what is forbidden (al-haram) differs among scholars. Some view it as zihar, some as divorce, some as an oath, and some differentiate based on the swearer's intention.

If the swearer intended divorce, then if the wife travels, divorce occurs, and he may take her back if this divorce does not complete three divorces. If he intended zihar, then zihar occurs, and it is not permissible for him to have intercourse with her before performing expiation. However, if he intended an oath or did not intend anything specific, then there is no blame on him for retracting his oath, and he must perform the expiation for an oath.

It must be noted that swearing by what is forbidden is not permissible. The permissible oath is to swear by Allah the Almighty.