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.
You mentioned many evil matters about your wife, some of which are enough to prove that she is disobedient and recalcitrant, such as disobeying you and traveling without your permission. We have already clarified how to treat a recalcitrant wife in fatwa 85402, so please refer to it.
You should follow these steps with her and seek the help of rational and righteous people from among your family and hers if necessary. If she is reformed and behaves well, then this is what is required, otherwise you should consider divorcing her. Perhaps divorce is the best solution when marital relations are impossible and when the objectives of marriage are not achieved.
Ibn Qudaamah said, “It could be that the relationship between the spouses is very bad and the continuity of the marriage is pure harm by obliging the husband to spend and provide accommodation and keeping the wife while there are bad marital relations and permanent disputes without any benefit, so this required legislating what would put an end to the marriage so that the harm resulting from it ends.”
However, if you want to be patient with her for the sake of the children and the like, then there is no harm in that. In that case, you may consider marrying a second wife provided that you are able to be just between them. For more benefit, please refer to fatwa 86818.
Finally, it should be noted that your mother-in-law should beware of being a reason for worsening the problem between her daughter and her husband. If she interferes, it should be for reconciliation, otherwise she should stay away.
We also advise not to get the children involved in the marital problems or to make them hate their father, as this leads to undutifulness to the father and severing the ties of kinship.
Allah knows best.