Is it permissible for the questioner to convince his mother to agree to his living in a house owned by his stepfather's third wife, despite his mother's refusal as she wishes him to live with her? Or is it permissible to live there without her consent?

There is no blame upon you for trying to persuade your mother to build you a home in the location your father suggested. Rather, you should do so. If she refuses, you are not obligated to obey her, as obedience to parents is only binding under three conditions:

1. It must not involve disobedience [to Allah]. 2. They must have a valid purpose. 3. It must not cause harm to the child. If it is difficult for the child but does not harm them, then it is obligatory; otherwise, it is not.

If the parents' command stems merely from foolishness and lack of intellect, then obedience to them is not obligatory.