What is the optimal course of action regarding continuous disputes between parents, and is it better to distance oneself from them, or to strive to fulfill their desire for separation?

You must be dutiful and kind to your parents, no matter their condition. Disagreements between spouses are natural, but they should not occur in front of the children. If you can reconcile them, then do so, for Allah the Almighty says: "There is no good in much of their private conversation, except for whoever enjoins charity or good or reconciliation between people." Explain to each of them their rights and duties with wisdom. If the problems escalate and marital life becomes untenable, Islam has permitted divorce, or khul' for the woman if the husband refuses to grant a divorce.