Is it permissible for the wife and her husband to leave the husband's family home to reside in an independent house, knowing that the husband finds it difficult to deal with his mother and ill sister, and despite the husband's attempts to convince his mother of this, which she totally rejected? And is this considered an act of disobedience from the husband towards his mother?

An independent dwelling is a right of the wife, and she is not obliged to live with the husband's relatives unless this was stipulated to her and she agreed. She has the right to demand an independent dwelling if she is harmed by living with them. The husband must provide an independent dwelling according to his ability, and he is not obliged to obey his mother if she prevents him from doing so, because obedience is only in what is good and permissible. It is preferable for the husband to strive to please his mother and obtain her consent if possible.