My father died recently and my mother is unable to live by herself. I want to host her but my wife refuses. I have other siblings but I want to take care of my mother myself as this is my duty. What should I do?

We understand the dilemma you are going through. Usually when it comes to these sorts of issues, the wife is reluctant to host her parents-in-law because of two reasons. The first is that she would feel confined in her own home where she loses her freedom to move around as she wishes. The second reason has to do with bearing the burden of serving them i.e. cooking, cleaning, laundry etc.
Thus, the wife could be reluctant to agree with the husband’s wish to bring his parents to stay with them. That being said, it should be clear that it is legally prohibited in Islamic law for the wife to prevent the husband from bringing his parents to live with them if they are unable to take care of themselves or find it difficult to live alone in their old age. It is also impermissible for the husband to force his wife to serve his parents and bear the burden of cleaning, cooking and so on as it is not her responsibility to do so. If the wife graciously agrees out of her good heart and free will, then she will be rewarded immensely for her righteous act but if she refuses and expresses her objection, then she will not be blameworthy and the husband has to respect her wishes.
In this case, the husband has to find a servant to aid his parents during their stay with him or to find a nearby apartment where his parents can live and find a servant to help them in their daily affairs. In the meantime, he can pay his parents regular visits and look after them.
If you cannot afford to buy an apartment for your mother or to provide her with a servant to look after her affairs and your wife refuses to serve her and decide to have her stay with you, it might be wise to ask the rest of your siblings if they can afford to host their mother with a welcoming heart.
At the end of the day, this is one of the matters which need great understanding and wisdom and an atmosphere full of compassion and mercy. You need to sit with your wife and quietly discuss her fears of having your mother in the home with you. You need to show her how much it really means to you to have your mother with you as she is unable to stay alone. In addition, you need to make sure that your mother feels welcomed in your home, that she is appreciated and that she is encouraged to stay with you, because it would hurt her feelings if she realizes that she is an unwanted burden that no one wishes to carry. May God guide you to the best solution and grant you and your family peace and happiness.
And God Almighty knows best.