What should I do about my parents repeatedly creating problems with the neighbors, and my father's resulting anger and my mother's cursing at me?

You must honor your parents and be kind to them, even if they treat you poorly. This is because Allah Almighty says: "Worship Allah and associate nothing with Him, and be good to parents." You must also try gently and wisely to prevent them from wronging neighbors, because harming a neighbor is forbidden, as stated in the Hadith (definition): "Whoever believes in Allah and the Last Day should not harm his neighbor." Remind them of the torment awaiting those who harm their neighbors, as in the Hadith: "There is no good in her; she is in the Fire," concerning the woman who harms her neighbors. Be patient in this and use various means of persuasion, for preventing them from wrongdoing is part of honoring them and helping them. You must strive to be good to your neighbors. As for moving away from your parents, it is not permissible except with their permission and provided that they do not need your service.