Is moving to an independent home considered an injustice to the mother, or is keeping the wife in the family home an injustice to her, especially with the wife's insistence on moving and the husband's refusal to leave his parents?

It is the wife's right that her husband provides her with a suitable, independent dwelling where she will not be subjected to harm. The husband is not permitted to compel her to live with his parents unless she consents. The proof for this is that al-Kasani said: "If the husband wishes to house her with a co-wife, or with his in-laws, such as his mother, sister, or daughter from another wife, or his relatives, and she refuses, then he must house her in a separate dwelling. This is because they might harm her and cause her distress by cohabiting. Her refusal is proof of harm and distress." Imam Malik was asked about a woman whom a man married, and he housed her with his father and mother, and she complained of harm therein. He replied: "He does not have the right to house her with them." It is obligatory upon you to honor your parents and treat them kindly. You can combine honoring your parents and treating your wife well by residing near them, or in their house, while providing an independent dwelling with its own facilities for your wife.