Is anything incumbent upon me if I move to a separate house near my mother's house, given my wife's discomfort with that?

If the new dwelling is suitable and independent, the wife does not have the right to refuse to move into it. Rather, it is not permissible for her to do so, even if the dwelling is in a house that includes the mother or others, because a house with separate rooms and facilities allows for co-wives to be housed within it without their consent. The husband should be wise in handling the matter and engage in dialogue with his wife, explaining the benefit to her, and that a righteous wife helps her husband in honoring his parents. Honoring parents is one of the best acts of worship. You must honor your mother and be good to her, especially with her old age and illness, for there is blessing in that in this world and the Hereafter.