What is the religious ruling on a husband remaining with a wife who refuses to serve and care for his mother, disobeys her husband in many matters, and has fallen short in her duty towards his sick mother, even though she fasts and prays a lot?

Do not divorce your wife, but explain to her that part of good spousal companionship is for the wife to be kind to her husband's family and to help him in his devotion to his parents and maintaining ties of kinship. You can also involve some righteous people to talk to her. If that does not work, then know that it is your wife's right to request a separate dwelling, which means a suitable and separate part of the house with its own facilities. If you provide her with that, she has no right to refuse; otherwise, she would be disobedient (nashiz). If that is not possible, then house your mother in a dwelling close to you to facilitate her care. If that is not feasible, and the wife refuses to return, then you may marry another woman who will help you in caring for your mother.