Is the sale contract considered valid if the parents agreed to sell an apartment to their children in exchange for gold owned by the mother, held by the father, and then returned to her, but the mother refused to hand over the gold after the sale was completed? And is it permissible for the children to benefit from the apartment and the gold with the father's consent?

The sale between your parents is invalid because it stipulates the return of the price after the sale. This condition invalidates the sale and contradicts its essence, as the Prophet (peace be upon him) forbade sales with conditions.

Therefore, the house belongs to your father and the gold belongs to your mother. You are permitted to benefit from them with their permission, and they will be inherited from them after death.