All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the wife travels for her personal need with her husband's permission, then there is a difference of opinion among the jurists about his obligation to spend on her.
The most preponderant opinion –Allah knows best –is that her right for her husband to spend on her is not waived as long as she travelled with his permission.
Shaykh Ibn 'Uthaymeen said:
“If she travels for her personal need with his permission, like if she says to him: ‘I want to consult a doctor’, or ‘I want to go to be tested in another college in Riyadh’, for example, and the husband gives her permission; then according to one view she loses her right for her husband to spend on her, but this is a weak view. The correct view, however, is that if the husband gives her permission, then she still has the right upon him to spend on her, because he is the one who agreed and gave her permission.” [End of quote]
Allah knows best.