Is the divorce Islamically valid in this case?

Your divorce of your wife afflicted with "leprosy" (vitiligo) is not valid, and is at the very least disliked, especially since you were aware of her illness and agreed to marry her. You should have fulfilled your promise. Furthermore, your obedience to your mother in divorcing your wife is not considered a righteous act, because obedience is only due in righteous matters. If you can take her back, then do so to correct your mistake.