All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is not permissible for a woman to go out of her husband's house without his permission, whether for a trip or for any other purpose. Therefore, this woman is wrong if she went out on this trip without the permission of her husband and thus she is considered a recalcitrant wife.
As regards this expression that her husband had uttered, it is probable that he threatened her with divorce if she travels, so she is not divorced unless he wishes to divorce her (fulfills his promise to divorce her).
It is also probable that he conditioned her divorce upon her travelling, in which case, it is a conditional divorce issued with a metaphor of divorce. For divorce to be effective with a metaphor, it depends on whether or not the husband had intended it. So, if he intended divorce, divorce takes place.
Also, if he did not utter the word ‘three times/thrice’, then divorce does not take place three times but only once. Hence, if this divorce is not preceded by two divorces, then she is still his wife and he has the right to take her back without a new contract as long she is still in her waiting period.
For more benefit on the kinds of divorce, please refer to Fatwa 82541.
Allaah Knows best.