Must the questioner agree with his wife to live in a separate home far from his mother, even though this would result in his mother living alone, and would this be considered disobedience to her?

The wife has the right to a suitable independent dwelling, meaning a separate part of the house with its own facilities. The wife does not have the right to request another dwelling if she already has a house with independent facilities, unless she suffers real harm from living next to the husband's mother.

Serving the mother is an obligation upon the children, not upon the wife. It is commendable for the wife to help her husband in honoring his mother.

If the mother harms the wife, the husband should gently advise his mother and strive to reconcile between them. If he is unable to do so, there is no blame upon the wife for not visiting the husband's mother. If the wife insists on a distant dwelling, there is no objection to fulfilling her request if it does not prevent the husband from honoring his mother. Otherwise, he should not comply, even if it leads to divorce.