Is a wife considered disobedient (nashiz) if she stipulated that she would not leave Medina unless with her consent, then cut ties with her husband and refused to meet him after a dispute between them, knowing that her husband visits her every two weeks and she does not go out to him, and does her right to maintenance and the maintenance of her children fall in this case?

Your wife erred by describing you as cowardly. However, if your statement to her that she is living on a "Misyar" marriage was sarcastic, then you also erred. Nevertheless, this does not justify her boycotting you and refusing to return to the marital home. By doing so, she becomes rebellious (nashiz), and her maintenance (nafaqa) falls away. As for the maintenance of the children, it does not fall away due to their mother's rebelliousness. If the wife stipulated that she not be taken out of her country, and the husband agreed, he is obliged to fulfill that. It is advised to seek to resolve the problem with wisdom and to seek the help of sensible people.