Are the wife's family entitled to demand the remaining portion of the dowry, even though the gold paid was considered part of it, in order to return the wife?

A man must pay his wife her mahr willingly, as Allah Almighty says: (And give women their dowries as a free gift). As for the gold given to the wife, if there is no agreement that it is part of the mahr, then reference should be made to the prevailing custom. If custom considers it mahr, then it is so; otherwise, it is a gift. Your intention alone does not change the ruling if it contradicts custom. It is advised to be forgiving, maintain good companionship, and not be overly strict regarding the mahr.