Is hastening marriage and living far from one's mother, as a way to avert temptation from oneself, considered disobedience to her and an injustice that warrants Allah's punishment, especially if the mother is not pleased with anything less than living next to her, which consequently delays the marriage?

Marriage is a good deed encouraged and urged by the Shari'a. If you are able to fulfill your mother's wish and live near her to gain her pleasure, then there is no doubt that this is better. If you cannot, try to convince her, seek Allah's help, and enlist the help of those who hold a respected position with her. If she insists on refusing without a legitimate reason, then there is no blame upon you for completing the marriage without her consent, and this is not considered disobedience. Obedience is in what is right, and it does not include obeying parents in what harms the child. We advise you to strive always to gain her pleasure.