Is a husband's refusal to accompany his wife to perform Umrah, under the pretext of going with his first wife later, then doing so shortly after his second wife's return, considered a sound and just action? And what should the wife do to overcome the feeling of injustice and oppression in this situation?

A husband must be just among his wives. It is not permissible for him to travel with some of them without others unless by drawing lots or with their consent. If he does so, he is sinful and must compensate the wife with whom he did not travel. She has the right to demand her due, or she may endure and seek her reward from Allah. She should advise him and explain the Shar'i ruling.