Am I obligated to host my mother in my husband's house, even though he is unwilling to have her there, and knowing that I cannot care for her due to my lack of proficiency in the language, and not having a job or a car?

Caring for an elderly mother who needs care is an obligation upon all her children. If the husband does not permit the mother to live with his wife or for his wife to serve her, then the husband's right takes precedence. It is not correct that the wife has a prior right to host her, though if the husband can be convinced to do so, it is good and he will receive a great reward. The mother's care is obligatory upon her financially able children, even if it means renting a house and hiring a maid, and it is not permissible to abandon her to destitution. Righteousness towards one's mother and kindness to her are among the greatest acts of nearness to Allah, and the children should compete in this. If the mother is abusive, it is obligatory to deal with her gently, be patient with her, and beware of being undutiful to her. It is not permissible to harm her, even if she harms you.