Is it permissible for the wife to object to her husband's family moving in with her in her independent home, especially since they have their own residence and the husband has another unmarried brother?

It is the wife's right that her husband provides her with private accommodation according to his means, provided that no harm befalls her, such as harassment from the husband's family or a co-wife. If the wife agrees to live with her husband's family to help her husband and to honor his parents, she will be rewarded, as Allah Almighty says: "And cooperate in righteousness and piety." If the husband's brother lives with them, she must be cautious so that he does not see any of her 'awrah (parts of the body that must be covered) or be alone with her, as he is a non-mahram to her.