Is a mother's supplication answered if she supplicates against her children while she is unjust to them, and is it permissible to separate parents in residence without divorce due to their frequent problems and the harm that this causes to the ill father, and what are the father's rights in this situation?

A mother's supplication against her child is answered, especially if he has wronged her or been disobedient. If you have not wronged your mother and are fulfilling her rights, then her supplication will not harm you. You should continue to be dutiful to her and advise her to stop supplicating against her children, as the Prophet, peace and blessings be upon him, forbade that, for he said: "Do not supplicate against yourselves, nor supplicate against your children, nor supplicate against your wealth, lest you coincide with an hour in which Allah is asked for a bounty and He grants it to you." As for separating the parents in residence to spare the father harm, there is no objection to it. It is obligatory to provide for the needy father and to care for him and serve him, either by yourselves or by providing someone to do so, while protecting him from any harm from the mother, such as insults.