What is the ruling regarding a wife remaining with her husband who utters divorce during disputes, then claims he did not intend divorce, and these incidents have been recurring for twenty years?

If your father's pronouncements of divorce were not explicit and he did not intend divorce thereby, then no divorce is binding upon him, and his word is accepted. However, if they were explicit (such as "You are divorced"), then his divorce is effective according to the general body of scholars, and his statement that he did not intend to effect a divorce holds no weight. If the matter is ambiguous, your parents are advised to seek a fatwa from a trustworthy source regarding the exact words he uttered.