Does a wife who has been entered upon deserve to be given the gold that her husband bought for her as part of her dowry, knowing that she betrayed him before marriage and after divorce while she was in her waiting period? And is it permissible for the husband to demand from her the money he spent on her and her family?

You did well to separate from the corrupt woman. You must pay her full dowry agreed upon in the contract, including the gold if it was part of the dowry. As for the money you spent as gifts for her and her family, you are not entitled to reclaim it after it has been received. You must repent to Allah and regret the sinful relationship, and increase your good deeds.