According to Halacha, what is one suppose to do in the case of abusive parents, considering that honoring one’s mother and father is a basic commandment in Judaism?
The Talmud records cases of abusive parents, and mentions that in spite of the parents’ behavior (parents who used to shame their children, and parents who used to damage them financially), the Sages would continue to honor their parents. This is also mentioned in Shulchan Aruch (Yoreh De’ah 240:3, 8).
However, it is very difficult, and almost impossible, to give due honor to abusive parents, and for the sake of the children, abusive parents should be distanced from their children. Distancing the parents would also solve the problem of honoring them. Indeed, several authorities advise that in circumstances where honoring parents is difficult/impossible, one should move out of the neighborhood, and try to avoid confrontation (for instance, see Aruch Hashulchan, 240:33, concerning a drunk parent).
If the parents are wicked (resha’im), authorities (Rambam and Tur) dispute whether or not there remains an obligation to honor them (see also Aruch Hashulchan, loc. cit.). Whether the parent would be considered “wicked” on account of his abusive behavior depends on the severity and nature of the abuse.