Is it permissible for a Muslim to ask Allah not to reunite him with his parents and family in Paradise, due to their mockery of him and their calling him "O black-skinned one, you came from the grave, and you are not created from clay"?

Your family mocking and belittling you is a grave transgression forbidden by Allah, who says: "O you who have believed, let not a people ridicule [another] people" (Quran 49:11). Similarly, it is not permissible to taunt someone about their color or similar attributes, as this is a characteristic of the Age of Ignorance (Jahiliyyah). And they have lied by saying, "You were not created from clay," for Allah Almighty has said: "And certainly did We create man from an extract of clay" (Quran 23:12). As for your supplication that Allah not gather you and them together in Paradise, if you mean by it a prayer that they enter Hellfire, then it is a supplication involving sin and the severance of kinship ties, which is not permissible.